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1
Gaudinskaitė, Danguolė. "Lietuvių kalbos sinonimiškų bendrašaknių asmenų pavadinimų darybos kategorijos." Vārds un tā pētīšanas aspekti: rakstu krājums = The Word: Aspects of Research: conference proceedings, no. 24 (December 2, 2020): 64–78. http://dx.doi.org/10.37384/vtpa.2020.24.064.
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In the Lithuanian language, persons are named by simple words and formations. The latter are divided into the categories of derivation according to their derivational meaning. The categories of derivation involve synonymous formations, i.e., derivative synonyms, and some formations are coherent in variance relation (they are derivative variants). The article aims to analyse the categories of derivation of synonymous conjugate personal names. The methods of derivational and semantic analysis, as well as calculation, were applied in the present research. The article discusses 1179 nominal personal names (out of these formations 338 rows of derivative synonyms and derivative variants were formed) collected from LKŽe, LKŽ, Volumes 1 and 2. After analysis of the empirical material, the following conclusions have been drawn: the formations of conjugate personal names were grouped into five categories of noun derivation: names of possessors of nominal characteristics (baldininkas, -ė – baldžius), names of persons according to profession (akmenininkas, -ė 1 / akmeninykas, -ė / akmeninkas, -ė / akmenykas, -ė – akmenkalis, -ė / akmenkalys, -ė – akmentašys, -ė), names according to origin (names of persons according to their place of origin and place of residence (adutiškėnas – adutiškietis, -ė); names of children according to their parents (antrasūnis – pasūnis – posūnis)), names according to gender differences (bernėnė – bernienė 1), names of collective nouns (bernynė – bernava – bernija). Only derivatives with suffixes and endings belong to the categories of noun derivation, but often persons are named by using derivatives with prefixes and compounds. Therefore, not only derivatives with suffixes and endings but also derivatives with prefixes and/or compounds belong to some rows of derivational synonyms (derivational variants). A big part of synonymous conjugate formations is composed of compounds (atlapaširdis, -ė – atviraširdis, -ė). These derivational synonyms (derivational variants) are not included in other traditional categories of derivation.
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Tsamparlis, Michael. "Derivation of Tensor Algebra as a Fundamental Operation—The Fermi Derivative in a General Metric Affine Space." Symmetry 17, no. 1 (January 7, 2025): 81. https://doi.org/10.3390/sym17010081.
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The aim of this work is to demonstrate that all linear derivatives of the tensor algebra over a smooth manifold M can be viewed as specific cases of a broader concept—the operation of derivation. This approach reveals the universal role of differentiation, which simplifies and generalizes the study of tensor derivatives, making it a powerful tool in Differential Geometry and related fields. To perform this, the generic derivative is introduced, which is defined in terms of the quantities Qk(i)(X). Subsequently, the transformation law of these quantities is determined by the requirement that the generic derivative of a tensor is a tensor. The quantities Qk(i)(X) and their transformation law define a specific geometric object on M, and consequently, a geometric structure on M. Using the generic derivative, one defines the tensor fields of torsion and curvature and computes them for all linear derivatives in terms of the quantities Qk(i)(X). The general model is applied to the cases of Lie derivative, covariant derivative, and Fermi derivative. It is shown that the Lie derivative has non-zero torsion and zero curvature due to the Jacobi identity. For the covariant derivative, the standard results follow without any further calculations. Concerning the Fermi derivative, this is defined in a new way, i.e., as a higher-order derivative defined in terms of two derivatives: a given derivative and the Lie derivative. Being linear derivative, it has torsion and curvature tensor. These fields are computed in a general affine space from the corresponding general expressions of the generic derivative. Applications of the above considerations are discussed in a number of cases. Concerning the Lie derivative, it is been shown that the Poisson bracket is in fact a Lie derivative. Concerning the Fermi derivative, two applications are considered: (a) the explicit computation of the Fermi derivative in a general affine space and (b) the consideration of Freedman–Robertson–Walker spacetime endowed with a scalar torsion field, which satisfies the Cosmological Principle and the computation of Fermi derivative of the spatial directions defining a spatial frame along the cosmological fluid of comoving observers. It is found that torsion, even in this highly symmetric case, induces a kinematic rotation of the space axes, questioning the interpretation of torsion as a spin. Finally it is shown that the Lie derivative of the dynamical equations of an autonomous conservative dynamical system is equivalent to the standard Lie symmetry method.
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Rehman, Hameed Ur, Maslina Darus, and Jamal Salah. "A Note on Caputo’s Derivative Operator Interpretation in Economy." Journal of Applied Mathematics 2018 (October 1, 2018): 1–7. http://dx.doi.org/10.1155/2018/1260240.
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We propound the economic idea in terms of fractional derivatives, which involves the modified Caputo’s fractional derivative operator. The suggested economic interpretation is based on a generalization of average count and marginal value of economic indicators. We use the concepts ofT-indicatorswhich analyses the economic performance with the presence of memory. The reaction of economic agents due to recurrence identical alteration is minimized by using the modified Caputo’s derivative operator of orderλinstead of integer order derivativen. The two sides of Caputo’s derivative are expressed by a brief time-line. The degree of attenuation is further depressed by involving the modified Caputo’s operator.
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Farid, Ghulam, and Zeeshan Afzal. "Further on quantum-plank derivatives and integrals in composite forms." Open Journal of Mathematical Analysis 6, no. 2 (December 30, 2022): 130–38. http://dx.doi.org/10.30538/psrp-oma2022.0118.
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In quantum-plank calculus, q-derivatives and h-derivatives are fundamental factors. Recently, a composite form of both derivatives is introduced and called q−h-derivative. This paper aims to present a further generalized notion of derivatives will be called (q ,p−h)-derivatives. This will produce q-derivative, h-derivative, q−h-derivative and (p,q)-derivative. Theory based on all aforementioned derivatives can be generalized via this new notion. It is expected, this paper will be useful and beneficial for researchers working in diverse fields of sciences and engineering.
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Gao, Zhe. "A Tuning Method via Borges Derivative of a Neural Network-Based Discrete-Time Fractional-Order PID Controller with Hausdorff Difference and Hausdorff Sum." Fractal and Fractional 5, no. 1 (March 14, 2021): 23. http://dx.doi.org/10.3390/fractalfract5010023.
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In this paper, the fractal derivative is introduced into a neural network-based discrete-time fractional-order PID controller in two areas, namely, in the controller’s structure and in the parameter optimization algorithm. The first use of the fractal derivative is to reconstruct the fractional-order PID controller by using the Hausdorff difference and Hausdorff sum derived from the Hausdorff derivative and Hausdorff integral. It can avoid the derivation of the Gamma function for the order updating to realize the parameter and order tuning based on neural networks. The other use is the optimization of order and parameters by using Borges derivative. Borges derivative is a kind of fractal derivative as a local fractional-order derivative. The chain rule of composite function is consistent with the integral-order derivative. It is suitable for updating the parameters and the order of the fractional-order PID controller based on neural networks. This paper improves the neural network-based PID controller in two aspects, which accelerates the response speed and improves the control accuracy. Two illustrative examples are given to verify the effectiveness of the proposed neural network-based discrete-time fractional-order PID control scheme with fractal derivatives.
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Gaudinskaitė, Danguolė. "Derivative Synonyms (Derivative Variants) of the Names of Persons Possessing Nominal Characteristics." Acta humanitarica academiae Saulensis 27 (April 3, 2025): 126–47. https://doi.org/10.15388/ahas.2020.9.
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In the Lithuanian language, the persons can be named by synonymous words (simple words and derivatives). A variety is revealed by lexical, derivative, syntactical synonyms as well as other language means. Derivative synonyms, which are one of the type of synonyms, are such derivatives of the Lithuanian language that have the same root, the same derivative meaning, but which are formed with different derivative means. Derivative variants should be distinguished from derivative synonyms: they are the derivatives formed from the same underlying word (or from the same underlying words) with the same derivative formative. They are formed by means of secondary derivative means, i.e. a vowel or a consonant of the root, variation of prefix, a connecting vowel, etc. The nominal derivatives indicating persons fall into five categories of noun formation. According to the features of the underlying words given to a derivative as well as derivative and lexical meanings, the compounds and derivatives with prefixes have synonymic relationship with the suffix and ending derivatives of traditional derivational categories. Applying the methods of derivative and semantic analysis as well as statistical, descriptive analytical, substitution methods, the derivatives of one derivative category – the names of the persons possessing nominal features – are discussed in the present article. The derivatives were drawn from LKŽ and LKŽe: 2,894 derivatives were selected, out of them 704 rows of derivative synonyms (derivative variants) were formed. Analysing the collected examples, it was revealed that the rows of derivative synonyms (derivative variants) can be divided into semantic groups according to some part of the body, similarity, character feature, etc. (barzdainis – barzdyla / barzdila – barzdylis – barzdylius – 2 barzdočius, -ė – barzdotis, -ė – barzdokas, -ė – barzdolė – barzdonas 1 – barzdukas 1 – barzduolis, -ė – barzdžius – velniabarzdis); according to family or mutual relationship (gentainis, -ė – gentininkas – gentaitis – gentbrolis); according to the meeting or gathering of people, participation in some joint events (vestuvininkas / vestuvinykas, -ė); according to inclination to one or another behaviour (juokininkas / juokinykas – juokorius – juokadaris, -ė / juokdarys, -ė / juokdaris, -ė / juokadara – juokbernis); according to favourite meal, drink or a person (druskininkas, -ė / druskinykas, -ė 2 – druskius, -ė – druskis, -ė); according to the place of participation somewhere, place of work (girtuvininkas, -ė / girtuvinykas, -ė / girtuvninkas, -ė / girtuvnykas, -ė); according to a person (or group of people), an organization, whose supporter or follower is a person (varpietis, -ė – varpininkas, -ė 2); according to a disease or an unhealthy part of the body (raupsuočius, -ė – raupsuotis, -ė); according to the received award or an achieved result (pirmūnas, -ė – pirmuolis, -ė); according to the work or rest time (2 nakti̇nis, -ė 2 – naktinyčia 8 – naktadarbis, -ė – nakti̇bauža 2 – 2 nakti̇žibis, -ė / nakti̇žiba – ži̇banaktis). The biggest part of derivatives is composed of derivatives with the suffixes (they make 70 per cent of the total number of all derivatives).
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Shapiro, Ilya L. "Covariant Derivative of Fermions and All That." Universe 8, no. 11 (November 4, 2022): 586. http://dx.doi.org/10.3390/universe8110586.
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We present detailed pedagogical derivation of covariant derivative of fermions and some related expressions, including commutator of covariant derivatives and energy-momentum tensor of a free Dirac field. On top of that, local conformal transformations for a Dirac fermion in curved spacetime are considered and we obtain the expression for the energy-momentum tensor on the cosmological background.
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Popov, Igor. "Scalar and vector division and derivatives vectors." Applied Mathematics and Control Sciences, no. 2 (June 29, 2018): 43–55. http://dx.doi.org/10.15593/2499-9873/2018.2.03.
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The work is devoted to the operations of differentiation in the space of vector fields and smooth functions. In mechanics, it is widely used derivative of a scalar function of the vector. To some extent, like it is determined by the derivative of the vector to another vector. However, formally interpreting the derivative as division differentials are entered in consideration of scalar and vector derived vector on another vector, which may have application to the solution of problems of mechanics. The definition of a derivative of a scalar vector field on another vector field. We prove a theorem on the representation of the scalar derivative in the form of a combination of partial derivatives. As a typical particular case is considered a scalar derivative in the radius vector, generating formalism linking it with the operator nabla. It is noted that in solving some problems in the mechanics to simplify the calculation coordinate system is chosen so that at least some vectors direction coincides with one of the coordinate axes. If it concerns the vector for derivation to be performed, in such cases, the formula for the three-dimensional case can not be used because some of this vector differentials are equal to zero. This circumstance makes it necessary to prove two theorems for the two-dimensional and one-dimensional case. The definition of a vector derivative of a vector field on another vector field. We prove a theorem on the representation of the derivative vector as a combination of partial derivatives. As a typical particular case considered vector derivative of the radius vector, generating formalism linking it with the operator nabla. We prove similar theorems for two-dimensional and one-dimensional case. We give examples of applications of these results to problems of mechanics.
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Lazopoulos, Anastasios K., and Dimitrios Karaoulanis. "Fractional Derivatives and Projectile Motion." Axioms 10, no. 4 (November 8, 2021): 297. http://dx.doi.org/10.3390/axioms10040297.
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Projectile motion is studied using fractional calculus. Specifically, a newly defined fractional derivative (the Leibniz L-derivative) and its successor (Λ-fractional derivative) are used to describe the motion of the projectile. Experimental data were analyzed in this study, and conclusions were made. The results of well-established fractional derivatives were also compared with those of L-derivative and Λ-fractional derivative, showing the many advantages of these new derivatives.
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Gaudinskaitė, Danguolė. "Sinonimiški bendrašakniai asmenų pagal profesiją pavadinimai: daryba, semantika, stilistika ir vartosena." Acta humanitarica academiae Saulensis 28 (December 30, 2021): 8–28. http://dx.doi.org/10.15388/ahas.2021.1.
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The nominal names of persons belong to different categories of formation (for example, the names of persons possessing nominal features, the names of persons by profession, etc.). A total of 1,266 conjugate synonymous nominal derivatives (or possessing one of the components of nominal words) naming the persons by profession were collected from the Dictionary of Lithuanian Language and its electronic version, out of them 386 rows of derivative synonyms (derivative variants) were formed. The derivatives were analysed in terms of formation, semantics, stylistics and usage. To achieve the aim, the methods of derivation, semantic analysis, calculation, descriptive-analytical, substitution were employed. The analysis of the material shows that the rows of derivative synonyms (derivative variants) formed from the names of the persons by profession and close to them derivatives can be divided into semantic groups: denoting an object required for business and work or craft (53,37 per cent of all derivatives); the person’s own business and work or craft, a person who makes a product (36,79 per cent of all derivatives); a place specific to the work (9,84 per cent of all derivatives).
 The analysis of the empirical material revealed that realia specific to ethnicity can be found in all semantic groups. Names of persons by profession can be associated with forest, plants, agriculture, animals, crafts, etc. The small number of usage of names of persons by profession suggests that they become uncharacteristic of the current language, either because the phenomenon itself no longer exists (then the names of persons also disappear) or because the phenomenon exists, but persons can be named differently (other formations are used).
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TARASOV, VASILY E. "FRACTIONAL DERIVATIVE AS FRACTIONAL POWER OF DERIVATIVE." International Journal of Mathematics 18, no. 03 (March 2007): 281–99. http://dx.doi.org/10.1142/s0129167x07004102.
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Definitions of fractional derivatives as fractional powers of derivative operators are suggested. The Taylor series and Fourier series are used to define fractional power of selfadjoint derivative operator. The Fourier integrals and Weyl quantization procedure are applied to derive the definition of fractional derivative operator. Fractional generalization of concept of stability is considered.
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Tseng, Yuan-Wei, and Jer-Guang Hsieh. "Optimal Control for a Family of Systems in Novel State Derivative Space Form with Experiment in a Double Inverted Pendulum System." Abstract and Applied Analysis 2013 (2013): 1–8. http://dx.doi.org/10.1155/2013/715026.
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Optimal control for a family of systems in novel state derivative space form, abbreviated as SDS systems in this study, is proposed. The first step in deriving optimal control laws for SDS systems is to form an augmented cost functional. It turns out that novel differential Lagrange multipliers must be used to adjoin SDS system constraints (namely, the dynamical equations of the control system) to the integrand of the original cost functional which is a function of state derivatives. This not only eases our derivation but also makes our derivation parallel to that for systems in standard state space form. We will show via a real electric circuit that optimal control for a class of descriptor systems with impulse modes can easily be carried out using our design method. It will be shown that linear quadratic regulator (LQR) design for linear time-invariant SDS systems using state derivative feedback can be obtained via an algebraic Riccati equation. Furthermore, this optimal state derivative feedback may also be implemented using an equivalent state feedback. This is useful in real situations when only states but not the state derivatives are available for measurement. The LQR design for a double inverted pendulum system is implemented to illustrate the use of our method.
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Bedair, A. H., Abd El-Wahab, A. M. El-Agrody, F. M. Ali, A. H. Halawa, and G. M. El-Sherbiny. "Binary heterocyclic systems containing the ethylideneamino linkage: synthesis of some new heterocyclic compounds bearing the naphtho-[2,1-b]furan moiety." Journal of the Serbian Chemical Society 71, no. 5 (2006): 459–69. http://dx.doi.org/10.2298/jsc0605459b.
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Ethylidene hydrazine (4a,b) and thiazolidin-4-one (5) derivatives were synthesized by the reaction of ethylidenethiosemicarbazide derivative (3a) with ?-haloketone/ethyl bromoacetate, respectively. Hetrocyclization of ethylideneacetohydrazide derivative (7) with o-phenolic aldehydes gave the corresponding coumarin derivatives (8,9). The interaction of 7 with acetylacetone afforded the corresponding pyridine derivative (10). Treatment of the arylidene derivative 11b with malononitrile afforded the corresponding pyran derivative (12). The new products 3-12 were subjected to IR, 1H NMR and mass spectra studies.
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Farayola, Musiliu Folarin, Sharidan Shafie, Fuaada Mohd Siam, Rozi Mahmud, and Suraju Olusegun Ajadi. "Mathematical modeling of cancer treatments with fractional derivatives: An Overview." Malaysian Journal of Fundamental and Applied Sciences 17, no. 4 (August 31, 2021): 389–401. http://dx.doi.org/10.11113/mjfas.v17n4.2062.
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This review article presents fractional derivative cancer treatment models to show the importance of fractional derivatives in modeling cancer treatments. Cancer treatment is a significant research area with many mathematical models developed by mathematicians to represent the cancer treatment processes like hyperthermia, immunotherapy, chemotherapy, and radiotherapy. However, many of these models were based on ordinary derivatives and the use of fractional derivatives is still new to many mathematicians. Therefore, it is imperative to review fractional cancer treatment models. The review was done by first presenting 22 various definitions of fractional derivative. Thereafter, 11 articles were selected from different online databases which included Scopus, EBSCOHost, ScienceDirect Journal, SpringerLink Journal, Wiley Online Library, and Google Scholar. These articles were summarized, and the used fractional derivative models were analyzed. Based on this analysis, the merit of modeling with fractional derivative, the most used fractional derivative definition, and the future direction for cancer treatment modeling were presented. From the results of the analysis, it was shown that fractional derivatives incorporated memory effects which gave it an advantage over ordinary derivative for cancer treatment modeling. Moreover, the fractional derivative is a general definition of all derivatives. Also, the fractional models can be applied to different cancer treatment procedures and the most used fractional derivative is the Caputo as well as its non-singular kernel versions. Finally, it was concluded that the future direction for cancer treatment modeling is the adoption of fractional derivative models corroborated with experimental or clinical data.
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Deppman, Airton, Eugenio Megías, and Roman Pasechnik. "Fractal Derivatives, Fractional Derivatives and q-Deformed Calculus." Entropy 25, no. 7 (June 30, 2023): 1008. http://dx.doi.org/10.3390/e25071008.
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This work presents an analysis of fractional derivatives and fractal derivatives, discussing their differences and similarities. The fractal derivative is closely connected to Haussdorff’s concepts of fractional dimension geometry. The paper distinguishes between the derivative of a function on a fractal domain and the derivative of a fractal function, where the image is a fractal space. Different continuous approximations for the fractal derivative are discussed, and it is shown that the q-calculus derivative is a continuous approximation of the fractal derivative of a fractal function. A similar version can be obtained for the derivative of a function on a fractal space. Caputo’s derivative is also proportional to a continuous approximation of the fractal derivative, and the corresponding approximation of the derivative of a fractional function leads to a Caputo-like derivative. This work has implications for studies of fractional differential equations, anomalous diffusion, information and epidemic spread in fractal systems, and fractal geometry.
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Plitzner, Patrick, Andreas Müller, Anton Güntsch, Walter Berendsohn, Andreas Kohlbecker, Norbert Kilian, Tilo Henning, and Ben Stöver. "The CDM Applied: Unit-Derivation, from Field Observations to DNA Sequences." Biodiversity Information Science and Standards 1 (August 16, 2017): e20366. https://doi.org/10.3897/tdwgproceedings.1.20366.
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Specimens form the falsifiable evidence used in plant systematics. Derivatives of specimens (including the specimen as the organism in the field) such as tissue and DNA samples play an increasing role in research. The EDIT Platform for Cybertaxonomy is a specialist's tool that allows to document and sustainably store all data that are used in the taxonomic work process, from field data to DNA sequences. The types of data stored can be very heterogeneous consisting of specimens, images, text data, primary data files, taxon assignments, etc. The EDIT Platform organizes the linking between such data by using a generic data model for representing the research process. Each step in the process is regarded as a derivation step and generates a derivative of the previous step. This could be a field unit having a specimen as its derivative or a specimen having a tissue sample as its derivative. Each derivation step also produces meta data storing who, when and how the derivation was done. The Platform's Common Data Model (CDM) and the applications build on the CDM library thus represent the first comprehensive implementation of the largely theoretical models developed in the late 1990ies (Berendsohn et al. 1999). In a pilot project research data about the genus <em>Campanula</em> (Kilian et al. 2015, FUB, BGBM 2012) was gathered and used to create a hierarchy of derivatives reaching from field data to DNA sequences. Additionally, the open source library for multiple sequence alignments LibrAlign (Stöver and Müller 2015) was used to integrate an alignment editor into the EDIT platform that allows to generate consensus sequences as derivatives of DNA sequences. The persistent storage of each link in the derivation process and the degree of detail on how the data and meta data are stored will speed up the research process, ease the reproducibility of research results and enhance sustainability of collections.
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Easton, CJ, and SC Peters. "Synthesis of Novel Cross-Linked Amino Acid Derivatives." Australian Journal of Chemistry 43, no. 1 (1990): 87. http://dx.doi.org/10.1071/ch9900087.
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Reactions of the derivatives of cysteine (6), serine (7) and lysine (8a), with the bromide (1), afforded the corresponding cross-linked amino acid derivatives (11), (12) and (13). Of the linked species (11)-(13), the cysteine derivative (11) was found to be the most stable under a variety of conditions. A mixture of the cross-linked serine derivative (12) and the cysteine derivative (6) in chloroform containing triethylamine reacted to give the cross-linked cysteine derivative (11) and the serine derivative (7). Similarly, a mixture of (13) and (6) in chloroform reacted to give (11).
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Moloi, Tankiso. "The nature of the derivative market transactions traded in the Johannesburg securities exchange." Risk Governance and Control: Financial Markets and Institutions 4, no. 3 (2014): 90–101. http://dx.doi.org/10.22495/rgcv4i3c1art3.
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The main objective of the study was to assess and understand the nature of derivative products traded in the Johannesburg Securities Exchange (JSE) by analysing daily transactions consisting of deals and contracts concluded, as well as notional values of derivatives traded in the review period. Analysed data found that the South African derivative market continues to grow and evolve with the consistent introduction of new derivative products such as the “can do” derivatives, IDX derivatives that are now being traded at the JSE. The evolvement and growth is confirmed by the fact that the total derivative deals in the JSE has also grown by 16.6% (CAGR) from 2006. The study further found that the equity index remains the largest derivative for both options and futures.
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Emmons, Brad, and Xiao Xiao. "A generalization of arithmetic derivative to p-adic fields and number fields." Notes on Number Theory and Discrete Mathematics 30, no. 2 (May 27, 2024): 357–82. http://dx.doi.org/10.7546/nntdm.2024.30.2.357-382.
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The arithmetic derivative is a function from the natural numbers to itself that sends all prime numbers to 1 and satisfies the Leibniz rule. The arithmetic partial derivative with respect to a prime p is the p-th component of the arithmetic derivative. In this paper, we generalize the arithmetic partial derivative to p-adic fields (the local case) and the arithmetic derivative to number fields (the global case). We study the dynamical system of the p-adic valuation of the iterations of the arithmetic partial derivatives. We also prove that for every integer n \geq 0, there are infinitely many elements with exactly n anti-partial derivatives. In the end, we study the p-adic continuity of arithmetic derivatives.
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Shi, Da, Ghulam Farid, Bakri Adam Ibrahim Younis, Hanaa Abu-Zinadah, and Matloob Anwar. "A Unified Representation of q- and h-Integrals and Consequences in Inequalities." Axioms 13, no. 4 (April 22, 2024): 278. http://dx.doi.org/10.3390/axioms13040278.
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This paper aims to unify q-derivative/q-integrals and h-derivative/h-integrals into a single definition, called q−h-derivative/q−h-integral. These notions are further extended on the finite interval [a,b] in the form of left and right q−h-derivatives and q−h-integrals. Some inequalities for q−h-integrals are studied and directly connected with well known results in diverse fields of science and engineering. The theory based on q-derivatives/q-integrals and h-derivatives/h-integrals can be unified using the q−h-derivative/q−h-integral concept.
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Cai, Min, and Changpin Li. "On Riesz derivative." Fractional Calculus and Applied Analysis 22, no. 2 (April 24, 2019): 287–301. http://dx.doi.org/10.1515/fca-2019-0019.
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Abstract This paper focuses on studying Riesz derivative. An interesting investigation on properties of Riesz derivative in one dimension indicates that it is distinct from other fractional derivatives such as Riemann-Liouville derivative and Caputo derivative. In the existing literatures, Riesz derivative is commonly considered as a proxy for fractional Laplacian on ℝ. We show the equivalence between Riesz derivative and fractional Laplacian on ℝn with n ≥ 1 in details.
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Burgess, VA, та CJ Easton. "Reaction of N-Benzoyl-2-bromoglycine Methyl Ester With Deprotonated Nitroalkanes: Synthesis of β-Nitro and α,β-Dehydro Amino Acid Derivatives". Australian Journal of Chemistry 41, № 7 (1988): 1063. http://dx.doi.org/10.1071/ch9881063.
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N-Benzoyl-2-bromoglycine methyl ester (1) reacted with the alkyl nitronates (2a-e) to give the corresponding β-nitro amino acid derivatives (4a-e). Elimination reactions of (4a-d) afforded the α,β-dehydro amino acid derivatives (5a-d). Treatment of the β- nitrovaline derivative (4b) with tributyltin hydride gave the valine derivative (8). Reduction of the β- nitroalanine derivative (4a) gave the β- aminoalanine derivative (9), characterized by hydrolysis to 2,3- diaminopropionic acid hydrochloride.
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Hasanah, Dahliatul. "On continuity properties of the improved conformable fractional derivatives." Jurnal Fourier 11, no. 2 (October 31, 2022): 88–96. http://dx.doi.org/10.14421/fourier.2022.112.88-96.
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The conformable fractional derivative has been introduced to extend the familiar limit definition of the classical derivative. Despite having many advantages compared to other fractional derivatives such as satisfying nice properties as classical derivative and easy to solve numerically, it also has disadvantages as it gives large error compared to Riemann-Liouville and Caputo fractional derivatives. Modified types of conformable derivatives have been proposed to overcome the shortcoming. The improved conformal fractional derivatives are declared to be better approximations of Riemann-Liouville and Caputo derivatives in terms of physical behavior. In this paper, properties concerning continuity of the improved conformable fractional derivative are investigated. We prove the relation between -differentiable and continuity of a function and corresponding interior extremum theorem. We also prove the properties close to Rolle’s Theorem and Mean Value Theorem for the improved conformable fractional derivatives.
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Khurshaid*, Adil, and Hajra Khurshaid. "Comparative Analysis and Definitions of Fractional Derivatives." Journal of Biomedical Research & Environmental Sciences 4, no. 12 (December 2023): 1684–88. http://dx.doi.org/10.37871/jbres1852.
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Fractional Calculus (FC) has emerged as a valuable tool in various fields. This study explores the historical development of (FC) and examines prominent definitions regarding Fractional Derivatives (FD), such as the Riemann-Liouville, Grunwald-Letnikov, Caputo Fractional Derivative, Katugampula derivatives, Caputo Fractional Derivative, Caputo-Fabrizio Fractional Derivative and as well as Atangana-Baleanu Fractional Derivative. It critically evaluates their strengths, weaknesses and implications on (FD) equations. The findings contribute to establishing a clearer understanding of Fractional Derivatives (FD) and guiding their appropriate use in practical scenarios. It investigates the impact of different definitions on the properties and behaviors of (FD), providing valuable insights for researchers.
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Zuhdi, Muhammad, Bakti Sukrisna, and Syamsuddin Syamsuddin. "IDENTIFICATION OF BURIED ARCHEOLOGICAL OBJECTS WITH RADIAL DERIVATIVES OF MICRO GRAVITY DATA." Indonesian Physical Review 2, no. 2 (May 30, 2019): 84. http://dx.doi.org/10.29303/ipr.v2i2.25.
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The development of recent gravimetric technology allows us to measure gravity anomalies with accuracy of micro Gal. Micro gravity is able to detect very small gravity anomalies such as anomaly due to buried archeological objects below the earth surface. Radial Derivatives of gravity data is used to sharpen anomaly due to lateral changes of density contrast. Horizontal derivatives carried out by previous researchers have some weaknesses, i.e. the loss of derivative values in certain directions and inconsistence values at the source boundary of the same anomaly edge. To solve the horizontal derivative problem, a radial derivative is made. Radial derivative is derivative of gravity anomaly over horizontal distance in the radial direction from a certain point which is considered as the center of anomaly. There are two kind of radial derivative i.e. First Radial Derivative (FRD) and Second Radial Derivative (SRD). Blade Pattern is another way to enrich the ability of SRD to detect boundary of anomaly source. Synthetic gravity data of buried archeological object was made by counting the response of forward modelling. All of programs and calculation of the models in this research is performed based on Matlab® program. The results of the tests on the synthetic data of the model show that the radial derivative is able to detect the boundaries in buried temples due to density contrast. The advantage of radial derivatives which is a horizontal derivative in the direction of radial compared to ordinary horizontal derivatives is the ability to detect vertical boundaries of various anomaly due to horizontal layers and capable of showing density contrast in almost all directions.
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İlhan, Esin, and İ. Onur Kıymaz. "A generalization of truncated M-fractional derivative and applications to fractional differential equations." Applied Mathematics and Nonlinear Sciences 5, no. 1 (March 31, 2020): 171–88. http://dx.doi.org/10.2478/amns.2020.1.00016.
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AbstractIn this paper, our aim is to generalize the truncated M-fractional derivative which was recently introduced [Sousa and de Oliveira, A new truncated M-fractional derivative type unifying some fractional derivative types with classical properties, Inter. of Jour. Analy. and Appl., 16 (1), 83–96, 2018]. To do that, we used generalized M-series, which has a more general form than Mittag-Leffler and hypergeometric functions. We called this generalization as truncated ℳ-series fractional derivative. This new derivative generalizes several fractional derivatives and satisfies important properties of the integer-order derivatives. Finally, we obtain the analytical solutions of some ℳ-series fractional differential equations.
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ETINKAYA, F. C. "A REVIEW ON THE EVOLUTION OF THE CONFORMABLE DERIVATIVE." Functional Differential Equations 29, no. 1 (2022): 23–37. http://dx.doi.org/10.26351/fde/29/1-2/2.
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This review paper focuses on the evolution of the conformable derivative. The review starts with expressing the idea behind the first research on the so-called conformable fractional derivative and examining some recent related papers. Then it continues mentioning some opposing papers which argue that the so-called conformable fractional derivative is actually not a fractional derivative because it lacks some of the agreed upon properties for fractional derivatives. The paper is closed by discussing another point of view on the theory of conformable derivatives.
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Galindo Illanes, Maritza Katherine, and Adriana Breda. "Processo de instrução do derivado aplicado a estudantes de engenharia de negócios no Chile." Uniciencia 38, no. 1 (July 31, 2024): 1–23. http://dx.doi.org/10.15359/ru.38-1.17.
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[Objective] The objective of this article is to present the results of the implementation of an instructional design for the teaching of the derivative for undergraduate students of Business Engineering in Chile. [Methodology] The participants in the study were ninety students of Applied Business Calculus at a Chilean university. The methodological design, based on the tools of the Ontosemiotic Approach to Mathematical Cognition and Instruction, consider various epistemic configurations in situations-problems concerning tangents, the calculation of derivatives from the rules for derivation, applications of the derivative for the calculation of maxima and minima, and analysis of graphs of functions. In addition, it integrates ICT into various activities. [Results] The results indicate that the instructional proposal for teaching the derivative overcomes some of students’ learning difficulties, as shown in various research studies. In particular, these include the difficulties that Business Engineering students have with the Euclidean conception of the tangent line, the interpretation of the derivative function and its geometric representation, the optimization of economic functions, and the application of the derivative to marginal functions. [Conclusions] It is concluded that the teaching and learning process is effective, in the sense that student learning for a specific engineering career is achieved by instruction that incorporates different interconnected epistemic configurations of the derivative, its different fields of problems, and contextual applications in their profession, together with the use of ICT resources.
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Parmikanti, Kankan, and Endang Rusyaman. "Grundwald-Letnikov Operator and Its Role in Solving Fractional Differential Equations." EKSAKTA: Berkala Ilmiah Bidang MIPA 23, no. 03 (September 15, 2022): 223–30. http://dx.doi.org/10.24036/eksakta/vol23-iss03/331.
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Leibnitz in 1663 introduced the derivative notation for the order of natural numbers, and then the idea of fractional derivatives appeared. Only a century later, this idea began to be realized with the discovery of the concepts of fractional derivatives by several mathematicians, including Riemann (1832), Grundwal, Fourier, and Caputo in 1969. The concepts in the definitions of fractional derivatives by Riemann-Liouville and Caputo are more frequently used than other definitions, this paper will discuss the Grunwald-Letnikov (GL) operator, which has been discovered in 1867. This concept is less popular when compared to the Riemann-Liouville and Caputo concepts, however, this concept is quite interesting because the concept of derivation is developed from the definition of ordinary derivatives. In this paper will be shown that the formulas for the fractional derivative using the GL concept are the same as the results obtained using the Riemann-Liouville and Caputo concepts. As a complement, we will give an example of solving a fractional differential equation using Modified Homotopy Perturbation Methods.
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Solovyov, Leonid A. "Full-profile refinement by derivative difference minimization." Journal of Applied Crystallography 37, no. 5 (September 11, 2004): 743–49. http://dx.doi.org/10.1107/s0021889804015638.
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A new method of full-profile refinement is developed on the basis of the minimization of the derivatives of the profile difference curve. The use of the derivatives instead of the absolute difference between the observed and calculated profile intensities allows refinement independently of the background. The procedure is tested on various powder diffraction data sets and is shown to be fully functional. Besides having the capability of powder diffraction structure analysis without modelling the background curve, the method is shown to allow the derivation of structure parameters of even higher quality than those obtained by Rietveld refinement in the presence of systematic errors in the model background function. The derivative difference minimization principles may be used in many different areas of powder diffraction and beyond.
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Holman, Glen, Carlos Correia, Lucian Pitt, and Akios Majoni. "The corporate use of derivatives by listed non-financial firms in Africa." Corporate Ownership and Control 11, no. 1 (2013): 671–90. http://dx.doi.org/10.22495/cocv11i1c7art5.
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This paper presents the results of an extensive analysis of derivative use by 692 companies in 20 countries across the African continent. The results show that 29% of non-financial companies in Africa use derivatives but that derivative use is dominated by firms within South Africa. The study finds that 54% of firms in South Africa use derivatives but only 5% of non-financial firms in Africa (excluding South Africa) use derivatives for hedging purposes. The majority of derivative use is directed toward the management of currency risks and the derivative instrument of choice is OTC forwards. Swaps are used to hedge interest rate risk and minimal use is made of OTC or exchange traded options and futures
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Novak, Oksana, Tetiana Osadcha, and Oleksandr Petruk. "CONCEPT AND CLASSIFICATION OF DERIVATIVE FINANCIAL INSTRUMENTS AS A METHODOLOGICAL PRECISION ON THEIR REGULATION IN THE FINANCIAL SERVICES MARKET." Baltic Journal of Economic Studies 5, no. 3 (August 1, 2019): 135. http://dx.doi.org/10.30525/2256-0742/2019-5-3-135-144.
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The urgency of the research topic is caused by the rapid growth of capital markets and the emergence of all new financial instruments, the complexity of their structure and the transition beyond the regulatory influence of supervisory authorities. Discussion issues on the identification of derivatives, as well as their certain types, create significant problems with their valuation, the correctness of accounting, and the application of regulatory measures. Inconsistency in the interpretation of derivative financial instruments nature and their certain types is also present in domestic legal acts. Therefore, until the elimination of these shortcomings, derivative financial instruments create additional risks for their owners – financial institutions, as well as for creditors and depositors. The purpose of the research, conducted in the article, lies in the clarification of derivatives nature and developing an appropriate classification of their types in order to its further use with a view of regulation. The methodological basis of the research. The methodological basis of the study is a dialectical approach to the understanding of the essence of derivative financial instruments; general scientific methods of knowledge of phenomena and processes (monographic, abstract-logical, synthesis, comparison, generalization), analysis of legal acts in the part of treatment of derivatives, derivative financial instruments and derivative securities, methods of grouping systematization and generalization in developing the classification of derivative financial instruments. Scientific results. It has been established that in order to maintain the stability of financial markets and their participants, the transformation of regulatory measures should be a permanent development and modification of the financial instruments that are being rotated. Various approaches to the interpretation of derivative financial instruments essence in normative legal acts and scientific literature have been analysed in order to improve the regulation of their issuance and circulation. This made it possible to streamline the conceptual apparatus and to group certain types of derivatives according to certain classification grounds. The basis for classification is the concept of “derivative financial instruments” as the broadest, which includes derivative securities and term contracts (derivatives). The concept of derivatives and derivative securities are delimited based on the study of terminology. It was established that derivatives are standard documents that certify the right and/or obligation to purchase or sell future securities, tangible or intangible assets, as well as funds or make payments on terms and conditions specified by them. However, in some cases, derivatives may acquire features of derivative securities, in particular, when issued through emission and freely traded in markets and bring income (losses) to their owner as a result of changes in their market value. The practical significance. The practical value of the research is the possibility of using the developed classification for the needs of emission regulation and the circulation of derivative financial instruments.
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Durur, Hülya, Ali Kurt, and Orkun Tasbozan. "New Travelling Wave Solutions for KdV6 Equation Using Sub Equation Method." Applied Mathematics and Nonlinear Sciences 5, no. 1 (April 10, 2020): 455–60. http://dx.doi.org/10.2478/amns.2020.1.00043.
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AbstractThis paper proposes obtaining the new wave solutions of time fractional sixth order nonlinear Equation (KdV6) using sub-equation method where the fractional derivatives are considered in conformable sense. Conformable derivative is an understandable and applicable type of fractional derivative that satisfies almost all the basic properties of Newtonian classical derivative such as Leibniz rule, chain rule and etc. Also conformable derivative has some superiority over other popular fractional derivatives such as Caputo and Riemann-Liouville. In this paper all the computations are carried out by computer software called Mathematica.
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Bayeğ, Selami, and Raziye Mert. "Generalized Hukuhara diamond-alpha derivative of fuzzy valued functions on time scales." Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics 74, no. 1 (December 5, 2024): 103–16. https://doi.org/10.31801/cfsuasmas.1577063.
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In the literature, the delta and nabla derivatives have been considered separately in the study of fuzzy number valued functions on time scales. In this paper, to unify these two derivatives for fuzzy number valued functions, we propose a new dynamic derivative called the diamond-alpha derivative, defined via the generalized Hukuhara difference. We establish several fundamental properties of the diamond-alpha derivative and investigate a particular class of fuzzy initial value problems on time scales with respect to this new derivative. Additionally, we provide numerical examples to illustrate our results.
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Kaya, U. "CAUCHY FRACTIONAL DERIVATIVE." Bulletin of the South Ural State University series "Mathematics. Mechanics. Physics" 12, no. 4 (2020): 28–32. http://dx.doi.org/10.14529/mmph200403.
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In this paper, we introduce a new sort of fractional derivative. For this, we consider the Cauchy's integral formula for derivatives and modify it by using Laplace transform. So, we obtain the fractional derivative formula F(α)(s) = L{(–1)(α)L–1{F(s)}}. Also, we find a relation between Weyl's fractional derivative and the formula above. Finally, we give some examples for fractional derivative of some elementary functions.
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Peng, Zhenhua, and Zhongping Wan. "Second-Order Composed Contingent Derivative of the Perturbation Map in Multiobjective Optimization." Asia-Pacific Journal of Operational Research 37, no. 02 (March 12, 2020): 2050002. http://dx.doi.org/10.1142/s0217595920500025.
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In view of the structural advantage of second-order composed derivatives, the purpose of this paper is to analyze quantitatively the behavior of perturbation maps for the first time by using this concept. First, new concepts of the second-order composed adjacent derivative and the second-order composed lower Dini derivative are introduced. Some relationships among the second-order composed contingent derivative, the second-order composed adjacent derivative and the second-order composed lower Dini derivative are discussed. Second, the relationships between second-order composed lower Dini derivable and Aubin property are provided. Third, by virtue of second-order composed contingent derivatives and the above relationships, some results concerning second-order sensitivity analysis are established without the assumption of the locally Lipschitz property or the locally Hölder continuity. Finally, we give some complete characterizations of second-order composed contingent derivatives of the perturbation maps.
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Smetona, Antanas. "Regarding the Verb “ĮTAKOTI”." Lietuvių kalba, no. 16 (December 30, 2021): 98–110. http://dx.doi.org/10.15388/lk.2021.5.
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The first attempts to correct the verb įtakoti and, naturally, its derivatives were observed in the 1970s. The main assumption for correcting (not to mention a certain “tradition” of correcting) is as follows: įtaka – an inflectional derivative from įtekėti, therefore suffixal derivatives with -oti are not possible from the systemic perspective. Thus, this is the influence of the Russian language. However, such an assumption is erroneous and originates from misinterpretation of derivation and history of correcting. The article aims to show that, on the one hand, įtaka → įtakoti can be seen as a regular model of derivation and, on the other hand, if the noun įtaka is considered to be a loan translation, there is no reason for thinking that it functions in the language differently from all the other a-stem nouns, which serve as basis for derivatives with the suffix -oti. 
 Abundancy of systemic examples of derivative verbs with the suffix -oti shows that the neologism įtakoti are in the same group with pasakoti and sąlygoti. They are prefixal verbs, i.e., derivatives with the suffix -oti from prefixal deverbative nouns: įtekėti → įtaka → įtakoti; nuimti → nuoma → nuomoti; pasekti → pasaka → pasakoti; pravežti → pravėža → pravėžoti; sulygti → sąlyga → sąlygoti. Therefore, correction of the verb įtakoti is not justified from the perspective of systemic word derivation.
 If įtaka is generally regarded as a part of derivational system of the Lithuanian language (and this is true, because it is a submorphemic loan translation, europeism, book neologism, although structurally successfully matching with examples of productive derivation models and likely to be influenced by analogous processes), its functioning in the Lithuanian language does not differ from other a-stem nouns – the derivational model of suffix -oti from the a-stem is abundant. The derivatives with this suffix are frequently derived from base nouns as well as from deverbatives, sometimes even from prefixal or concrete or even abstract nouns; the meaning of derivation does not fall out of the context here. Names of persons with the suffix -tojas are formed in big numbers and a systemic way from derivatives with the suffix -oti and with the root of verb – pasakotojas, sąlygotojas, nuomotojas, pravėžotojas, įtakotojas.
 The suffix -oti is successfully used to derive verbs from prefixal deverbatives, although some limitations can also be observed – the derivative with suffix -oti is not made from įlanka. This leads only to one conclusion – a theoretical approach to a model of derivation has to be all-encompassing and considering various possibilities. Moreover, exaggerated support/denial of a certain model leads to erroneous generalizations. In general, in such complex systems (a) there is always a considerable diversity of non-systemic usage – due to different frequency of usage as well as because of historical and cognitive reasons, (b) there are always blank spaces that appear due to formally different but semantically identical or very close derivation models, which usually have to be evaluated not only from the systemic point of view but also considering a common sense of language and live speech of people (aras/erelis, siuvėjas/siūtojas, rašytojas/rašėjas, pasakoti/padangoti…).
 Due to all the aforesaid circumstances, the verb įtakoti is a systemic derivative/loan translation, which occupies a reasonable place in one or another derivation sub-system in the Lithuanian language as well as a fact of live speech, which does not contradict the systemic structure of language.
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Diethelm, Kai, Roberto Garrappa, Andrea Giusti, and Martin Stynes. "Why fractional derivatives with nonsingular kernels should not be used." Fractional Calculus and Applied Analysis 23, no. 3 (June 25, 2020): 610–34. http://dx.doi.org/10.1515/fca-2020-0032.
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AbstractIn recent years, many papers discuss the theory and applications of new fractional-order derivatives that are constructed by replacing the singular kernel of the Caputo or Riemann-Liouville derivative by a non-singular (i.e., bounded) kernel. It will be shown here, through rigorous mathematical reasoning, that these non-singular kernel derivatives suffer from several drawbacks which should forbid their use. They fail to satisfy the fundamental theorem of fractional calculus since they do not admit the existence of a corresponding convolution integral of which the derivative is the left-inverse; and the value of the derivative at the initial time t = 0 is always zero, which imposes an unnatural restriction on the differential equations and models where these derivatives can be used. For the particular cases of the so-called Caputo-Fabrizio and Atangana-Baleanu derivatives, it is shown that when this restriction holds the derivative can be simply expressed in terms of integer derivatives and standard Caputo fractional derivatives, thus demonstrating that these derivatives contain nothing new.
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SUZUKI, MASUO. "GENERAL FORMULATION OF QUANTUM ANALYSIS." Reviews in Mathematical Physics 11, no. 02 (February 1999): 243–65. http://dx.doi.org/10.1142/s0129055x9900009x.
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A general formulation of noncommutative or quantum derivatives for operators in a Banach space is given on the basis of the Leibniz rule, irrespective of their explicit representations such as the Gâteaux derivative or commutators. This yields a unified formulation of quantum analysis, namely the invariance of quantum derivatives, which are expressed by multiple integrals of ordinary higher derivatives with hyperoperator variables. Multivariate quantum analysis is also formulated in the present unified scheme by introducing a partial inner derivation and a rearrangement formula. Operator Taylor expansion formulas are also given by introducing the two hyperoperators [Formula: see text] and [Formula: see text] with the inner derivation δA:Q↦[A,Q]≡AQ-QA. Physically the present noncommutative derivatives express quantum fluctuations and responses.
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Hattaf, Khalid. "On Some Properties of the New Generalized Fractional Derivative with Non-Singular Kernel." Mathematical Problems in Engineering 2021 (May 27, 2021): 1–6. http://dx.doi.org/10.1155/2021/1580396.
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This paper presents some new formulas and properties of the generalized fractional derivative with non-singular kernel that covers various types of fractional derivatives such as the Caputo–Fabrizio fractional derivative, the Atangana–Baleanu fractional derivative, and the weighted Atangana–Baleanu fractional derivative. These new properties extend many recent results existing in the literature. Furthermore, the paper proposes some interesting inequalities that estimate the generalized fractional derivatives of some specific functions. These inequalities can be used to construct Lyapunov functions with the aim to study the global asymptotic stability of several fractional-order systems arising from diverse fields of science and engineering.
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Rajratana Maroti Kamble and Pramod Ramakant Kulkarni. "Extended fractional derivative: Some results involving classical properties and applications." Scientific Temper 15, no. 04 (December 20, 2024): 3026–33. https://doi.org/10.58414/scientifictemper.2024.15.4.09.
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In this paper, considering the classical definition of derivative in the limit form, we can define a new fractional derivative called the extended fractional derivative, which depends upon two parameters α and a. For this new fractional derivative, we have proved the properties of classical derivatives such as the product rule, the quotient rule, the chain rule, Rolle’s and Lagrange’s mean value theorems, etc., which are nor satisfied by the existing fractional derivatives defined by Riemann Liouville, Caputo, Grunwald. Moreover, we have defined the extended fractional integral and proved some related results. Solve extended fractional differential equation.
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Hattaf, Khalid. "A New Mixed Fractional Derivative with Applications in Computational Biology." Computation 12, no. 1 (January 4, 2024): 7. http://dx.doi.org/10.3390/computation12010007.
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This study develops a new definition of a fractional derivative that mixes the definitions of fractional derivatives with singular and non-singular kernels. This developed definition encompasses many types of fractional derivatives, such as the Riemann–Liouville and Caputo fractional derivatives for singular kernel types, as well as the Caputo–Fabrizio, the Atangana–Baleanu, and the generalized Hattaf fractional derivatives for non-singular kernel types. The associate fractional integral of the new mixed fractional derivative is rigorously introduced. Furthermore, a novel numerical scheme is developed to approximate the solutions of a class of fractional differential equations (FDEs) involving the mixed fractional derivative. Finally, an application in computational biology is presented.
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Babenko, V. F., and M. S. Churilova. "On inequalities of Kolmogorov type for fractional derivatives of functions defined on the real domain." Researches in Mathematics 16 (February 7, 2021): 28. http://dx.doi.org/10.15421/240804.
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We obtain new inequalities that generalize known result of Geisberg, which was obtained for fractional Marchaud derivatives, to the case of higher derivatives, at that the fractional derivative is a Riesz one. The inequality with second higher derivative is sharp.
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Manjushree, S. "A Derivative is a Risk Hedging Tool from Investor Perspective." Shanlax International Journal of Commerce 8, no. 3 (July 1, 2020): 39–44. http://dx.doi.org/10.34293/commerce.v8i3.3131.
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Derivatives products provide certain important economic benefits such as risk management or redistribution of risk away from risk-averse investors towards those more willing and able to bear the risk. Derivatives also help price discovery, i.e., the process of determining the price level for any asset based on supply and demand. These functions of derivatives help inefficient capital allocation in the economy; at the same time, their misuse also poses a threat to the stability of the financial sector and the overall economy. In the mid-1990s, India started reviving the exchangetraded commodity derivatives market. It introduced a variety of instruments in the foreign exchange derivatives market, while exchange-traded financial derivatives were introduced in 2001. Given India’s experience in informal derivatives trading, the exchange-traded derivatives were quick to pick up substantial volumes. This paper presents the concept of derivative and types of derivative products and how the investor perceives the derivative instrument as a risk-hedging tool in shivamooga city. The study is selected 70 respondents and used percentage analysis. The result obtained from the study reveals that the investor prefers a derivative is a risk-hedging tool.
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Fedorov, Vladimir E., Marina V. Plekhanova, and Elizaveta M. Izhberdeeva. "Initial Value Problems of Linear Equations with the Dzhrbashyan–Nersesyan Derivative in Banach Spaces." Symmetry 13, no. 6 (June 11, 2021): 1058. http://dx.doi.org/10.3390/sym13061058.
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Among the many different definitions of the fractional derivative, the Riemann–Liouville and Gerasimov–Caputo derivatives are most commonly used. In this paper, we consider the equations with the Dzhrbashyan–Nersesyan fractional derivative, which generalizes the Riemann–Liouville and the Gerasimov–Caputo derivatives; it is transformed into such derivatives for two sets of parameters that are, in a certain sense, symmetric. The issues of the unique solvability of initial value problems for some classes of linear inhomogeneous equations of general form with the fractional Dzhrbashyan–Nersesyan derivative in Banach spaces are investigated. An inhomogeneous equation containing a bounded operator at the fractional derivative is considered, and the solution is presented using the Mittag–Leffler functions. The result obtained made it possible to study the initial value problems for a linear inhomogeneous equation with a degenerate operator at the fractional Dzhrbashyan–Nersesyan derivative in the case of relative p-boundedness of the operator pair from the equation. Abstract results were used to study a class of initial boundary value problems for equations with the time-fractional Dzhrbashyan–Nersesyan derivative and with polynomials in a self-adjoint elliptic differential operator with respect to spatial variables.
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Doungmo Goufo, Emile Franc, and Sunil Kumar. "Shallow Water Wave Models with and without Singular Kernel: Existence, Uniqueness, and Similarities." Mathematical Problems in Engineering 2017 (2017): 1–9. http://dx.doi.org/10.1155/2017/4609834.
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After the recent introduction of the Caputo-Fabrizio derivative by authors of the same names, the question was raised about an eventual comparison with the old version, namely, the Caputo derivative. Unlike Caputo derivative, the newly introduced Caputo-Fabrizio derivative has no singular kernel and the concern was about the real impact of this nonsingularity on real life nonlinear phenomena like those found in shallow water waves. In this paper, a nonlinear Sawada-Kotera equation, suitable in describing the behavior of shallow water waves, is comprehensively analyzed with both types of derivative. In the investigations, various fixed-point theories are exploited together with the concept of Piccard K-stability. We are then able to obtain the existence and uniqueness results for the models with both versions of derivatives. We conclude the analysis by performing some numerical approximations with both derivatives and graphical simulations being presented for some values of the derivative order γ. Similar behaviors are pointed out and they concur with the expected multisoliton solutions well known for the Sawada-Kotera equation. This great observation means either of both derivatives is suitable to describe the motion of shallow water waves.
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Journal, Baghdad Science. "Synthesis and Characterization of New Heterocyclic Compounds from 2, 5- dimercapto -1, 3, 4-Thiadiazole and Their Resins." Baghdad Science Journal 13, no. 2 (June 5, 2016): 275–88. http://dx.doi.org/10.21123/bsj.13.2.275-288.
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In this research, a new 1, 3, 4-Thiadiazole derivatives have been synthesized by many heterocyclic reactions. Starting from (2, 5 – dimercapto -1, 3, 4-Thiadiazole) a variety of derivatives have been synthesis. Compound (1) was synthesized by the reaction of hydrazine hydrate with carbon disulphide in absolute ethanol. The compound (1) was reacted with 1, 2-dibromoethane in presence of alkali ethanol to give the compound (2). The compound (3) was formed from the reaction of compound (2) with hydrazine hydrate. Schiff base (4) was obtained by reacting of compound (3) with the compound (p-hydroxybenzaldehyde) in absolute ethanol. A variety of phenolic Schiff base (Methylolic, Etheric, and Epoxy) derivatives have been synthesized. Methylolic derivative was synthesized by the reaction of Schiff base (4) with formaldehyde in tetrahydrofuran (THF). Etheric derivative was formed from the reaction of a methylolic Schiff base (5) with saturated alcohol (Methanol).Epoxy derivative was synthesized by the reaction of epichlorohydrine with etheric derivative (6) .The last step of this research was the preparation of a composite material from mixing the Epoxy resin derivative(7), TiO2and morpholine via ring opening. All these derivatives were verified by using (FT-IR, UV) spectra photometer and 1H-NMR spectra. Also, these derivatives were characterized using elemental analysis (C.H.N.S) .
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Guswanto, Bambang Hendriya, Leony Rhesmafiski Andini, and Triyani Triyani. "On Conformable, Riemann-Liouville, and Caputo fractional derivatives." Bulletin of Applied Mathematics and Mathematics Education 2, no. 2 (December 19, 2022): 59–64. http://dx.doi.org/10.12928/bamme.v2i2.7072.
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This article compares conformable fractional Derivative with Riemann-Liouville and Caputo fractional derivative by comparing solutions to fractional ordinary differential equations involving the three fractional derivatives via the numerical simulations of the solutions. The result shows that conformable fractional derivative can be used as an alternative to Riemann-Liouville and Caputo fractional derivative for order α with 1/2<α<1.
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Özkan, Ozan, and Ali Kurt. "Exact solutions of fractional partial differential equation systems with conformable derivative." Filomat 33, no. 5 (2019): 1313–22. http://dx.doi.org/10.2298/fil1905313o.
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Main goal of this paper is to have the new exact solutions of some fractional partial differential equation systems (FPDES) in conformable sense. The definition of conformable fractional derivative (CFD) is similar to the limit based definition of known derivative. This derivative obeys both rules which other popular derivatives do not satisfy such as derivative of the quotient of two functions, the derivative product of two functions, chain rule and etc. By using conformable derivative it is seen that the solution procedure for (PDES) is simpler and more efficient.
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Smith, Mark R. "Basic Derivatives for the Oil and Gas Company." Alberta Law Review 39, no. 1 (August 1, 2001): 152. http://dx.doi.org/10.29173/alr511.
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This article provides a general overview of some of the basic derivatives available to oil and gas companies. The author begins by defining what a derivative is and briefly summarizing four basic kinds derive, of derivatives. The author offers other examples of derivative products and illustrates how oil and gas companies can design and utilize these products to meet their individual needs. The article includes a discussion of the 1SDA master agreement, which is used for most over-the-counter derivative contracts. As well, the article outlines some of the key regulatory provisions governing and affecting derivatives, with particular emphasis on Alberta.