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Journal articles on the topic 'Theorem on Partial'

Author: Grafiati

Published: 18 May 2024

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1

ABBAS, MUJAHID, BASIT ALI, and GABRIELA PETRUSEL. "Fixed points of set-valued contractions in partial metric spaces endowed with a graph." Carpathian Journal of Mathematics 30, no. 2 (2014): 129–37. http://dx.doi.org/10.37193/cjm.2014.02.15.

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Hassen, Abbas and Vetro [H. Aydi, M. Abbas and C. Vetro, Partial Hausdorff metric and Nadler’s fixed point theorem on partial metric spaces, Topology and its App., 159 (2012), 3234–3242] introduced the concept of a partial Hausdorff-Pompeiu metric and proved Nadler’s theorem in this context. Employing the notion of a partial Hausdorff-Pompeiu metric, we investigate the existence of fixed points of set-valued mappings on partial metric spaces endowed with a graph. Our results extend some recent theorems in the literature.

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Karapınar, Erdal, Nabi Shobkolaei, Shaban Sedghi, and Mansour Vaezpour. "A common fixed point theorem for cyclic operators on partial metric spaces." Filomat 26, no. 2 (2012): 407–14. http://dx.doi.org/10.2298/fil1202407k.

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In this paper, we prove a common fixed point theorem for two self-mappings satisfying certain conditions over the class of partial metric spaces. In particular, the main theorem of this manuscript extends some well-known fixed point theorems in the literature on this topic.

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3

Pogromsky, Alexander Yu. "A partial synchronization theorem." Chaos: An Interdisciplinary Journal of Nonlinear Science 18, no. 3 (September 2008): 037107. http://dx.doi.org/10.1063/1.2959145.

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4

Lipasov, Pavel P., and Vladimir N. Shchennikov. "Stability with Respect to a Part of Variables under Constant Perturbations of the Partial Equilibrium Position of Differential Equation Nonlinear Systems." Mordovia University Bulletin 28, no. 3 (September 20, 2018): 344–51. http://dx.doi.org/10.15507/0236-2910.028.201803.344-351.

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Introduction. It is impossible to take into account all the forces acting in the process of mathematical modeling of dynamic processes. In order that mathematical models the most accurately describe the dynamic processes, they must include the terms that correspond the constant perturbations. These problems arise in applied tasks. In this paper we consider the case when the system allows for the partial equilibrium position. The aim of this work is to prove the stability theorem for the partial equilibrium position at constant perturbations, which are small at every instant. Materials and Methods. The research objects are nonlinear systems of differential equations that allow for a partial equilibrium position. Using the second Lyapunov method, there are proved the stability theorems for the constant perturbations of the partial equilibrium position, which are small at every instant. Results. Together with the introduction of stability for a part of the variables, it has become necessary to introduce stability for the part of phase variables under constant perturbations. The first stability theorem of the part of phase variables under constant perturbations was obtained by A. S. Oziraner. In this work, we prove a theorem of the stability of the constant perturbations of the partial equilibrium position, small at every instant. It should be noted that there is no stability theorems of constant perturbations for the partial equilibrium position. Thus, the theorem proved in this work is of a pioneer nature. Conclusions. The theorem 3 proved in the work is the development of the mathematical theory of stability. The results of this work are applicable in the mechanics of controlled motion, nonlinear system.

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Hannabou, Mohamed, Khalid Hilal, and Ahmed Kajouni. "Existence and Uniqueness of Mild Solutions to Impulsive Nonlocal Cauchy Problems." Journal of Mathematics 2020 (November 12, 2020): 1–9. http://dx.doi.org/10.1155/2020/5729128.

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In this paper, a class of nonlocal impulsive differential equation with conformable fractional derivative is studied. By utilizing the theory of operators semigroup and fractional derivative, a new concept on a solution for our problem is introduced. We used some fixed point theorems such as Banach contraction mapping principle, Schauder’s fixed point theorem, Schaefer’s fixed point theorem, and Krasnoselskii’s fixed point theorem, and we derive many existence and uniqueness results concerning the solution for impulsive nonlocal Cauchy problems. Some concrete applications to partial differential equations are considered. Some concrete applications to partial differential equations are considered.

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Al-hawasy, Jamil Amir, and Safaa J. Mohammed Al-Qaisi. "The Continuous Classical Boundary Optimal Control of a Couple Nonlinear Elliptic Partial Differential Equations with State Constraints." Al-Mustansiriyah Journal of Science 30, no. 1 (August 15, 2019): 143. http://dx.doi.org/10.23851/mjs.v30i1.464.

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This paper is concerned with, the proof of the existence and the uniqueness theorem for the solution of the state vector of a couple of nonlinear elliptic partial differential equations using the Minty-Browder theorem, where the continuous classical boundary control vector is given. Also the existence theorem of a continuous classical boundary optimal control vector governing by the couple of nonlinear elliptic partial differential equation with equality and inequality constraints is proved. The existence of the uniqueness solution of the couple of adjoint equations associated with the considered couple of the state equations with equality and inequality constraints is studied. The necessary conditions theorem and the sufficient conditions theorem for optimality of the couple of nonlinear elliptic equations with equality and inequality constraints are proved using the Kuhn-Tucker-Lagrange multipliers theorems

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7

Ge, Zheng-Ming, and Jung-Kui Yu. "Pragmatical Asymptotical Stability Theorems on Partial Region and for Partial Variables with Applications to Gyroscopic Systems." Journal of Mechanics 16, no. 4 (December 2000): 179–87. http://dx.doi.org/10.1017/s1727719100001842.

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ABSTRACTFor a long time, all stability theorems are concerned with the stability of the zero solution of the differential equations of disturbed motion on the whole region of the neighborhood of the origin. But for various problems of dynamical systems, the stability is actually on partial region. In other words, the traditional mathematical model is unmatched with the dynamical reality and artificially sets too strict demand which is unnecessary. Besides, although the stability for many problems of dynamical systems may not be mathematical asymptotical stability, it is actual asymptotical stability — namely “pragmatical asymptotical stability” which can be introduced by the concept of probability. In order to fill the gap between the traditional mathematical model and dynamical reality of various systems, one pragmatical asymptotical stability theorem on partial region and one pragmatical asymptotical stability theorem on partial region for partial variables are given and applications for gyroscope systems are presented.

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8

Tarasenko, Stepan. "Sperner's Theorem." Modeling Control and Information Technologies, no. 5 (November 21, 2021): 87–89. http://dx.doi.org/10.31713/mcit.2021.27.

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In the course of this work the analysis of the proofs of the simple case of the Sperner Theorem was carried out, the approaches to the proof of the complicated case were proposed, the partial cases of multisets were considered, the theorem for these partial cases was proved, the generalized theorem was proved for some partial cases. (the number of n - element multisets of k - element multiset), developed a small program to graphically show this fact, proved the bimonotonicity of this function. Also, in the course of this work, one of the possible applications of this theorem was considered, namely, the «Procedure for secret distribution», but the applied potential of the theorem does not end there.

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Guo, Shuangjian, Xiaohui Zhang, Yuanyuan Ke, and Yizheng Li. "Enveloping actions and duality theorems for partial twisted smash products." Filomat 34, no. 10 (2020): 3217–27. http://dx.doi.org/10.2298/fil2010217g.

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In this paper, we first generalize the theorem about the existence of an enveloping action to a partial twisted smash product. Then we construct a Morita context between the partial twisted smash product and the twisted smash product related to the enveloping action. Finally, we present versions of the duality theorems of Blattner-Montgomery for partial twisted smash products.

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10

Góźdź, A., and M. Góźdź. "Spectral theorem and partial symmetries." Physics of Atomic Nuclei 75, no. 10 (October 2012): 1195–202. http://dx.doi.org/10.1134/s1063778812100055.

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11

Stoltenberg-Hansen, Viggo, and John V. Tucker. "Computable and Continuous Partial Homomorphisms on Metric Partial Algebras." Bulletin of Symbolic Logic 9, no. 3 (September 2003): 299–334. http://dx.doi.org/10.2178/bsl/1058448675.

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AbstractWe analyse the connection between the computability and continuity of functions in the case of homomorphisms between topological algebraic structures. Inspired by the Pour-El and Richards equivalence theorem between computability and boundedness for closed linear operators on Banach spaces, we study the rather general situation of partial homomorphisms between metric partial universal algebras. First, we develop a set of basic notions and results that reveal some of the delicate algebraic, topological and effective properties of partial algebras. Our main computability concepts are based on numerations and include those of effective metric partial algebras and effective partial homomorphisms. We prove a general equivalence theorem that includes a version of the Pour-El and Richards Theorem, and has other applications. Finally, the Pour-El and Richards axioms for computable sequence structures on Banach spaces are generalised to computable partial sequence structures on metric algebras, and we prove their equivalence with our computability model based on numerations.

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12

FIORANI, EMANUELE. "GEOMETRICAL ASPECTS OF INTEGRABLE SYSTEMS." International Journal of Geometric Methods in Modern Physics 05, no. 03 (May 2008): 457–71. http://dx.doi.org/10.1142/s0219887808002886.

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We review some basic theorems on integrability of Hamiltonian systems, namely the Liouville–Arnold theorem on complete integrability, the Nekhoroshev theorem on partial integrability and the Mishchenko–Fomenko theorem on noncommutative integrability, and for each of them we give a version suitable for the noncompact case. We give a possible global version of the previous local results, under certain topological hypotheses on the base space. It turns out that locally affine structures arise naturally in this setting.

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Carlson, Timothy J. "Ranked partial structures." Journal of Symbolic Logic 68, no. 4 (December 2003): 1109–44. http://dx.doi.org/10.2178/jsl/1067620176.

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AbstractThe theory of ranked partial structures allows a reinterpretation of several of the standard results of model theory and first-order logic and is intended to provide a proof-theoretic method which allows for the intuitions of model theory. A version of the downward Löwenheim-Skolem theorem is central to our development. In this paper we will present the basic theory of ranked partial structures and their logic including an appropriate version of the completeness theorem.

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14

Reibiger, A. "Generalizations of Blakesley's Source Shift Theorem." Advances in Radio Science 7 (May 18, 2009): 67–71. http://dx.doi.org/10.5194/ars-7-67-2009.

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Abstract. It is shown that the well-known Voltage Source Shift Theorem due to Blakesley and its dual version, the Current Source Shift Theorem as well as the rules for the transformation of networks with loops of capacitors or cut sets of inductors into networks without such loops or cutsets, resp., and the relationships between capacitance coefficients and partial capacitors are special cases of general theorems on the terminal behavior of networks. The proof of these theorems is based on the theory of terminal behavior of networks. For these proofs we do not need the substitution theorem with its strong uniqueness assumptions. This fact is an essential advantage in comparison to the original proof given by Chua and Green.

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15

Truong, Công Nghê. "On non-linear elliptic equations and the stability of soap film." Bulletin of the Australian Mathematical Society 57, no. 3 (June 1998): 353–61. http://dx.doi.org/10.1017/s0004972700031750.

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We use an Inverse Mapping Theorem for Sobolev chains to obtain a number of existence theorems for non-linear elliptic partial differential equations with general order. We then apply one of these theorems to prove the stability of a soap film.

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16

Thakur, Ramkrishna, and S. K. Samanta. "A Study on Some Fundamental Properties of Continuity and Differentiability of Functions of Soft Real Numbers." Advances in Fuzzy Systems 2018 (2018): 1–8. http://dx.doi.org/10.1155/2018/6429572.

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We introduce a new type of functions from a soft set to a soft set and study their properties under soft real number setting. Firstly, we investigate some properties of soft real sets. Considering the partial order relation of soft real numbers, we introduce concept of soft intervals. Boundedness of soft real sets is defined, and the celebrated theorems like nested intervals theorem and Bolzano-Weierstrass theorem are extended in this setting. Next, we introduce the concepts of limit, continuity, and differentiability of functions of soft sets. It has been possible for us to study some fundamental results of continuity of functions of soft sets such as Bolzano’s theorem, intermediate value property, and fixed point theorem. Because the soft real numbers are not linearly ordered, several twists in the arguments are required for proving those results. In the context of differentiability of functions, some basic theorems like Rolle’s theorem and Lagrange’s mean value theorem are also extended in soft setting.

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17

ÉSIK, Z., and T. HAJGATÓ. "Dagger extension theorem." Mathematical Structures in Computer Science 21, no. 5 (August 22, 2011): 1035–66. http://dx.doi.org/10.1017/s0960129511000326.

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Partial iterative theories are algebraic theories such that for certain morphisms f the equation ξ = f ⋅ 〈ξ, 1p〉 has a unique solution. Iteration theories are algebraic theories satisfying a certain set of identities. We investigate some similarities between partial iterative theories and iteration theories.In our main result, we give a sufficient condition ensuring that the partially defined dagger operation of a partial iterative theory can be extended to a totally defined operation so that the resulting theory becomes an iteration theory. We show that this general extension theorem can be instantiated to prove that every Elgot iterative theory with at least one constant morphism 1 → 0 can be extended to an iteration theory. We also apply our main result to theories equipped with an additive structure.

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18

Karapınar, Erdal, and Wasfi Shatanawi. "On Weakly -Contractive Mappings in Ordered Partial Metric Spaces." Abstract and Applied Analysis 2012 (2012): 1–17. http://dx.doi.org/10.1155/2012/495892.

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We introduce the notion of weakly -contractive mappings in ordered partial metric spaces and prove some common fixed point theorems for such contractive mappings in the context of partially ordered partial metric spaces under certain conditions. We give some common fixed point results of integral type as an application of our main theorem. Also, we give an example and an application of integral equation to support the useability of our results.

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19

Simpson, Stephen G. "Partial realizations of Hilbert's program." Journal of Symbolic Logic 53, no. 2 (June 1988): 349–63. http://dx.doi.org/10.1017/s0022481200028309.

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§0. Introduction. What follows is a write-up of my contribution to the symposium “Hilbert's Program Sixty Years Later” which was sponsored jointly by the American Philosophical Association and the Association for Symbolic Logic. The symposium was held on December 29,1985 in Washington, D. C. The panelists were Solomon Feferman, Dag Prawitz and myself. The moderator was Wilfried Sieg. The research which I discuss here was partially supported by NSF Grant DMS-8317874.I am grateful to the organizers of this timely symposium on an important topic. As a mathematician I particularly value the opportunity to address an audience consisting largely of philosophers. It is true that I was asked to concentrate on the mathematical aspects of Hilbert's program. But since Hilbert's program is concerned solely with the foundations of mathematics, the restriction to mathematical aspects is really no restriction at all.Hilbert assigned a special role to a certain restricted kind of mathematical reasoning known as finitistic. The essence of Hilbert's program was to justify all of set-theoretical mathematics by means of a reduction to finitism. It is now well known that this task cannot be carried out. Any such possibility is refuted by Gödel's theorem. Nevertheless, recent research has revealed the feasibility of a significant partial realization of Hilbert's program. Despite Gödel's theorem, one can give a finitistic reduction for a substantial portion of infinitistic mathematics including many of the best-known nonconstructive theorems. My purpose here is to call attention to these modern developments.

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20

Xue, Wei, Ping Xi, and Yi Duo Wang. "Transformation Formulas between Bézier Curve and Partial said-Ball Curve." Applied Mechanics and Materials 397-400 (September 2013): 2487–90. http://dx.doi.org/10.4028/www.scientific.net/amm.397-400.2487.

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Based on previous work, which presented theorems and algorithms for generating a new type of generalized Ball curve (Partial Said-Ball curve), the present study supplements the transformation formula from a Bézier curve to a Partial Said-Ball curve and prove the corresponding theorem. All the results are useful for the application of generalized Ball curves and their popularization in Computer Aided Geometric Design.

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21

Saluja, G. S. "Some Fixed Point Results in Partial Metric Spaces Under Contractive Type Mappings." Journal of the Indian Mathematical Society 87, no. 3-4 (July 1, 2020): 219. http://dx.doi.org/10.18311/jims/2020/25453.

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In this paper, we establish some fixed point theorems and a coincidence point theorem for contractive type mappings in the framework of complete partial metric spaces and give some examples in support of our results. The results presented in this paper extend and generalize several results from the existing literature.

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22

Aksoy, Asuman, and Mario Martelli. "Mixed Partial Derivatives and Fubini's Theorem." College Mathematics Journal 33, no. 2 (March 2002): 126. http://dx.doi.org/10.2307/1558995.

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23

Bessis, D. N., and F. H. Clarke. "Partial subdifferentials, derivates and Rademacher’s Theorem." Transactions of the American Mathematical Society 351, no. 7 (March 10, 1999): 2899–926. http://dx.doi.org/10.1090/s0002-9947-99-02203-5.

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Aksoy, Asuman, and Mario Martelli. "Mixed Partial Derivatives and Fubini's Theorem." College Mathematics Journal 33, no. 2 (March 2002): 126–30. http://dx.doi.org/10.1080/07468342.2002.11921930.

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25

Balakrishnan, R., and T. Kavaskar. "Interpolation theorem for partial Grundy coloring." Discrete Mathematics 313, no. 8 (April 2013): 949–50. http://dx.doi.org/10.1016/j.disc.2013.01.018.

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26

SMITH, JONATHAN D. H. "EVANS' NORMAL FORM THEOREM REVISITED." International Journal of Algebra and Computation 17, no. 08 (December 2007): 1577–92. http://dx.doi.org/10.1142/s0218196707004323.

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Evans defined quasigroups equationally, and proved a Normal Form Theorem solving the word problem for free extensions of partial Latin squares. In this paper, quasigroups are redefined as algebras with six basic operations related by triality, manifested as coupled right and left regular actions of the symmetric group on three symbols. Triality leads to considerable simplifications in the proof of Evans' Normal Form Theorem, and makes it directly applicable to each of the six major varieties of quasigroups defined by subgroups of the symmetric group. Normal form theorems for the corresponding varieties of idempotent quasigroups are obtained as immediate corollaries.

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27

Ghazal, Bayan, Rania Saadeh, and Abdelilah K. Sedeeg. "Solving Partial Integro-Differential Equations via Double Formable Transform." Applied Computational Intelligence and Soft Computing 2022 (December 26, 2022): 1–15. http://dx.doi.org/10.1155/2022/6280736.

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In this study, we present a new double integral transform called the double formable transform. Several properties and theorems related to existing conditions, partial derivatives, the double convolution theorem, and others are presented. Additionally, we use a convolution kernel to solve linear partial integro-differential equations (PIDE) by using the double formable transform. By solving numerous cases, the double formable transform’s ability to turn the PIDE into an algebraic equation that is simple to solve is demonstrated.

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Pavlovic, Vladimir, Dejan Ilic, and Vladimir Rakocevic. "An extension of two fixed point theorems of Fisher to partial metric spaces." Filomat 29, no. 10 (2015): 2339–45. http://dx.doi.org/10.2298/fil1510339p.

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In S.G. Matthews [Partial metric topology, in: Proc. 8th Summer Conference on General Topology and Applications, in: Ann. New York Acad. Sci., vol. 728, 1994, pp. 183-197], the author introduced and studied the concept of partial metric space, and obtained a Banach type fixed point theorem on complete partial metric spaces. The present paper forms part of the study of possible extensions of metric fixed point results to the context of partial metric spaces, in particular two theorems due to Fisher. The theory is illustrated by some examples.

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Kamont, Z., and S. Kozieł. "First Order Partial Functional Differential Equations with Unbounded Delay." gmj 10, no. 3 (September 2003): 509–30. http://dx.doi.org/10.1515/gmj.2003.509.

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Abstract The phase space for nonlinear hyperbolic functional differential equations with unbounded delay is constructed. The set of axioms for generalized solutions of initial problems is presented. A theorem on the existence and continuous dependence upon initial data is given. The Cauchy problem is transformed into a system of integral functional equations. The existence of solutions of this system is proved by the method of successive approximations and by using theorems on integral inequalities. Examples of phase spaces are given.

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30

Endou, Noboru, Yasunari Shidama, and Masahiko Yamazaki. "Integrability and the Integral of Partial Functions from R into R1." Formalized Mathematics 14, no. 4 (January 1, 2006): 207–12. http://dx.doi.org/10.2478/v10037-006-0023-y.

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Integrability and the Integral of Partial Functions from R into R1 In this paper, we showed the linearity of the indefinite integral the form of which was introduced in [11]. In addition, we proved some theorems about the integral calculus on the subinterval of [a,b]. As a result, we described the fundamental theorem of calculus, that we developed in [11], by a more general expression.

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31

Zhang, B. G., and Jian-She Yu. "Comparison and linearized oscillation theorems for a nonlinear partial difference equation." ANZIAM Journal 42, no. 4 (April 2001): 552–60. http://dx.doi.org/10.1017/s144618110001227x.

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AbstractConnections between a linear partial difference equation with constant coefficients and a nonlinear partial difference equation are established by means of a comparison theorem and a continuous dependence of parameters theorem. A linearized oscillation theorem is also established as an application.

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32

Gągol, Adam. "Pattern avoidance in partial words over a ternary alphabet." Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica 69, no. 1 (November 30, 2015): 73. http://dx.doi.org/10.17951/a.2015.69.1.73.

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Blanched-Sadri and Woodhouse in 2013 have proven the conjecture of Cassaigne, stating that any pattern with \(m\) distinct variables and of length at least \(2^m\) is avoidable over a ternary alphabet and if the length is at least \(3\cdot 2^{m-1}\) it is avoidable over a binary alphabet. They conjectured that similar theorems are true for partial words – sequences, in which some characters are left “blank”. Using method of entropy compression, we obtain the partial words version of the theorem for ternary words.

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Kane, T. R., and S. Djerassi. "Integrals of Linearized Differential Equations of Motion of Mechanical Systems; Part I: Linearized Differential Equations." Journal of Applied Mechanics 54, no. 3 (September 1, 1987): 656–60. http://dx.doi.org/10.1115/1.3173084.

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Part I of this paper deals with relationships between integrals of a set of nonlinear differential equations and integrals of equations obtained from such a set by a process of linearization. The terms “total linearization,” “reduction,” and “partial linearization” are introduced, a theorem is stated and proved in connection with each of these, and the use of each theorem is illustrated by means of an example. In Part II, the theorems are applied to differential equations of motion of mechanical systems.

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Fortunato, Westher Manricky Bernardes, and Dassael Fabricio dos Reis Santos. "An Application of the Browder-Minty Theorem in a Problem of Partial Differential Equations." REMAT: Revista Eletrônica da Matemática 6, no. 1 (December 30, 2019): 1–12. http://dx.doi.org/10.35819/remat2020v6i1id3524.

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In this work, we will show existence of weak solution for a semilinear elliptic problem using as main tool the Browder-Minty Theorem. First, we will make a brief introduction about basic theory of the Sobolev Spaces to support our study and provide sufficient tools for the development of our work. Then we will take a quick approach on the Browder-Minty Theorem and use this result to show the existence of at least one weak solution to an elliptic Partial Differential Equations (PDE) problem whose nonlinearity, denoted by f, is a known function. For this, in addition to the already mentioned results, we will also use as study tools: Embedding Sobolev Theorems, Linear Continuous Operators Theory, Poincaré Inequality and Hölder Inequality.

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35

Towsner, Henry. "Partial impredicativity in reverse mathematics." Journal of Symbolic Logic 78, no. 2 (June 2013): 459–88. http://dx.doi.org/10.2178/jsl.7802070.

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AbstractIn reverse mathematics, it is possible to have a curious situation where we know that an implication does not reverse, but appear to have no information on how to weaken the assumption while preserving the conclusion (other than reducing all the way to the tautology of assuming the conclusion). A main cause of this phenomenon is the proof of a sentence from the theory . Using methods based on the functional interpretation, we introduce a family of weakenings of and use them to give new upper bounds for the Nash-Williams Theorem of wqo theory and Menger's Theorem for countable graphs.

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Bitimkhan, S., and D. T. Alibieva. "Partial best approximations and the absolute Cesaro summability of multiple Fourier series." BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS 103, no. 3 (September 30, 2021): 4–12. http://dx.doi.org/10.31489/2021m3/4-12.

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The article is devoted to the problem of absolute Cesaro summability of multiple trigonometric Fourier series. Taking a central place in the theory of Fourier series this problem was developed quite widely in the one-dimensional case and the fundamental results of this theory are set forth in the famous monographs by N.K. Bari, A. Zigmund, R. Edwards, B.S. Kashin and A.A. Saakyan [1–4]. In the case of multiple series, the corresponding theory is not so well developed. The multidimensional case has own specifics and the analogy with the one-dimensional case does not always be unambiguous and obvious. In this article, we obtain sufficient conditions for the absolute summability of multiple Fourier series of the function f ∈ Lq(Is) in terms of partial best approximations of this function. Four theorems are proved and four different sufficient conditions for the |C; β¯|λ-summability of the Fourier series of the function f are obtained. In the first theorem, a sufficient condition for the absolute |C; β¯|λ- summability of the Fourier series of the function f is obtained in terms of the partial best approximation of this function which consists of s conditions, in the case when β1 = ... = βs = 1/q'. Other sufficient conditions are obtained for double Fourier series. Sufficient conditions for the |C; β1; β2|λ-summability of the Fourier series of the function f ∈ Lq(I2) are obtained in the cases β1 = 1/q', −1 < β2 < 1/q'(in the second theorem), 1/q'< β1 < +∞, β2 = 1/q', (in the third theorem), −1 < β1 < 1/q', 1/q' < β2 < +∞ (in the fourth theorem).

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37

Chen, Franklin M., Nada Abdi, and Nolan Torres. "Applications of the Partial Molar Volume Concept in Whisky and Gin Dilutions with Water." Journal of Distilling Science 1, no. 1 (December 27, 2021): 8–16. http://dx.doi.org/10.61855/jds0101.01.

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The meaning of the partial molar volume, the analytical methods for finding the partial molar volumes and the additivity theorem of the partial molar volumes are explained. The additivity theorem of the partial molar volume is used for whisky alcohol strength dilutions and for single shot or multi-shots for gin in both flavor dilution with GNS and alcohol strength dilution.

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38

Nagy, Bela. "Partial isometries and a general spectral theorem." Advances in Operator Theory 4, no. 2 (April 2019): 351–68. http://dx.doi.org/10.15352/aot.1804-1355.

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Zhang, Liangyun, and Ruifang Niu. "MASCHKE-TYPE THEOREM FOR PARTIAL SMASH PRODUCTS." International Electronic Journal of Algebra 19, no. 19 (June 1, 2016): 49. http://dx.doi.org/10.24330/ieja.266192.

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Lindström, Per. "A theorem on partial conservativity in arithmetic." Journal of Symbolic Logic 76, no. 1 (March 2011): 341–47. http://dx.doi.org/10.2178/jsl/1294171003.

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AbstractImproving on a result of Arana, we construct an effective family (φr ∣ r ϵ ℚ ∩ [0,1]) of Σn-conservative Πn sentences, increasing in strength as r decreases, with the property that ¬φp is Πn-conservative over PA + φq whenever p < q. We also construct a family of Σn sentences with properties as above except that the roles of Σn and Πn are reversed. The latter result allows to re-obtain an unpublished result of Solovay, the presence of a subset order-isomorphic to the reals in every non-trivial end-segment of every branch of the E-tree, and to generalize it to analogues of the E-tree at higher levels of the arithmetical hierarchy.

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41

Krishnakumar, R., and R. Livingston. "Fixed Point Theorem in Partial Metric Spaces." International Journal of Scientific Research in Mathematical and Statistical Sciences 5, no. 4 (August 31, 2018): 384–88. http://dx.doi.org/10.26438/ijsrmss/v5i4.384388.

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42

Blanchet-Sadri, F., and S. Duncan. "Partial words and the critical factorization theorem." Journal of Combinatorial Theory, Series A 109, no. 2 (February 2005): 221–45. http://dx.doi.org/10.1016/j.jcta.2004.09.002.

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43

Lawson, M. V. "Extending partial isomorphisms and McAlister's covering theorem." Semigroup Forum 48, no. 1 (December 1994): 18–27. http://dx.doi.org/10.1007/bf02573650.

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44

Krylov, N. V. "Hörmander’s theorem for stochastic partial differential equations." St. Petersburg Mathematical Journal 27, no. 3 (March 30, 2016): 461–79. http://dx.doi.org/10.1090/spmj/1398.

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Goldwasser, J. L., A. J. W. Hilton, D. G. Hoffman, and Sibel Özkan. "Hall's theorem and extending partial latinized rectangles." Journal of Combinatorial Theory, Series A 130 (February 2015): 26–41. http://dx.doi.org/10.1016/j.jcta.2014.10.007.

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Hu, Zhanrong, and Zhen Jin. "Almost Automorphic Mild Solutions to Neutral Parabolic Nonautonomous Evolution Equations with Nondense Domain." Discrete Dynamics in Nature and Society 2013 (2013): 1–10. http://dx.doi.org/10.1155/2013/183420.

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Combining the exponential dichotomy of evolution family, composition theorems for almost automorphic functions with Banach fixed point theorem, we establish new existence and uniqueness theorems for almost automorphic mild solutions to neutral parabolic nonautonomous evolution equations with nondense domain. A unified framework is set up to investigate the existence and uniqueness of almost automorphic mild solutions to some classes of parabolic partial differential equations and neutral functional differential equations.

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47

Niu, Boshan. "Definition of Residue Theorem and its Basic Applications." Highlights in Science, Engineering and Technology 72 (December 15, 2023): 965–70. http://dx.doi.org/10.54097/77gdf824.

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This paper explains the fundamentality of residue theorem in complex analysis integration termed contour integral. It also illustrates the importance of this theorem, followed by applying it in both mathematics and other fields where several typical examples coming from different fields are chosen. The paper introduces some basic definitions and theorems to support and finally prove residue theorem. Then two simple applications of residue theorem are presented. One is a contour integral of a fractional function with one singularity inside the contour. It can be solved by using partial fraction technique, then directly finding the residue at the singularity, and finally applying residue theorem to calculate for the result. The other one is a contour integral of a reciprocal of sine function with one singularity inside. This problem can be solved by finding the Laurent series of the integrand, thus finding the residue needed. However, the residue is the coefficient of negative-one-degree term of the singularity, and the value of the integral can be achieved by substituting the residue into the formula of the residue theorem.

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Wei, Xian-Biao, Yan-Hsiou Cheng, and Yu-Ping Wang. "The Partial Inverse Spectral and Nodal Problems for Sturm–Liouville Operators on a Star-Shaped Graph." Mathematics 10, no. 21 (October 26, 2022): 3971. http://dx.doi.org/10.3390/math10213971.

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We firstly prove the Horváth-type theorem for Sturm–Liouville operators on a star-shaped graph and then solve a new partial inverse nodal problem for this operator. We give some algorithms to recover this operator from a dense nodal subset and prove uniqueness theorems from paired-dense nodal subsets in interior subintervals having a central vertex. In particular, we obtain some uniqueness theorems by replacing the information of nodal data on some fixed edge with part of the eigenvalues under some conditions.

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Souayah, Nizar, and Mehdi Mrad. "On Fixed-Point Results in Controlled Partial Metric Type Spaces with a Graph." Mathematics 8, no. 1 (December 26, 2019): 33. http://dx.doi.org/10.3390/math8010033.

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Recently, Mlaiki et al. introduced the notion of a controlled metric type space which is a generalization of the b-metric space. In this work, we define the controlled partial metric type space and give some fixed-point theorems for extensions of Kannan contraction in this space with suitable conditions. Moreover, as an application, we derive a fixed-point theorem for graphic contraction on the considered metric space endowed with a graph.

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Ávila, Jesús, Víctor Marín, and Héctor Pinedo. "Isomorphism Theorems for Groupoids and Some Applications." International Journal of Mathematics and Mathematical Sciences 2020 (February 26, 2020): 1–10. http://dx.doi.org/10.1155/2020/3967368.

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Using an algebraic point of view we present an introduction to the groupoid theory; that is, we give fundamental properties of groupoids as uniqueness of inverses and properties of the identities and study subgroupoids, wide subgroupoids, and normal subgroupoids. We also present the isomorphism theorems for groupoids and their applications and obtain the corresponding version of the Zassenhaus Lemma and the Jordan-Hölder theorem for groupoids. Finally, inspired by the Ehresmann-Schein-Nambooripad theorem we improve a result of R. Exel concerning a one-to-one correspondence between partial actions of groups and actions of inverse semigroups.

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