Articles de revues : « Degenerine »

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TAVERNARAKIS, NEKTARIOS, et MONICA DRISCOLL. « Degenerins ». Annals of the New York Academy of Sciences 940, n^o 1 (25 janvier 2006) : 28–41. http://dx.doi.org/10.1111/j.1749-6632.2001.tb03664.x.

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Hanzer, Marcela. « Degenerate Eisenstein series for symplectic groups ». Glasnik Matematicki 50, n^o 2 (30 décembre 2015) : 289–332. http://dx.doi.org/10.3336/gm.50.2.04.

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Kellenberger, Stephan, et Laurent Schild. « Epithelial Sodium Channel/Degenerin Family of Ion Channels : A Variety of Functions for a Shared Structure ». Physiological Reviews 82, n^o 3 (7 janvier 2002) : 735–67. http://dx.doi.org/10.1152/physrev.00007.2002.

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The recently discovered epithelial sodium channel (ENaC)/degenerin (DEG) gene family encodes sodium channels involved in various cell functions in metazoans. Subfamilies found in invertebrates or mammals are functionally distinct. The degenerins in Caenorhabditis elegansparticipate in mechanotransduction in neuronal cells, FaNaC in snails is a ligand-gated channel activated by neuropeptides, and the Drosophila subfamily is expressed in gonads and neurons. In mammals, ENaC mediates Na+ transport in epithelia and is essential for sodium homeostasis. The ASIC genes encode proton-gated cation channels in both the central and peripheral nervous system that could be involved in pain transduction. This review summarizes the physiological roles of the different channels belonging to this family, their biophysical and pharmacological characteristics, and the emerging knowledge of their molecular structure. Although functionally different, the ENaC/DEG family members share functional domains that are involved in the control of channel activity and in the formation of the pore. The functional heterogeneity among the members of the ENaC/DEG channel family provides a unique opportunity to address the molecular basis of basic channel functions such as activation by ligands, mechanotransduction, ionic selectivity, or block by pharmacological ligands.

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Chalfie, Martin, Monica Driscoll et Mingxia Huang. « Degenerin similarities ». Nature 361, n^o 6412 (février 1993) : 504. http://dx.doi.org/10.1038/361504a0.

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Nohel, John A. « A class of one-dimensional degenerate parabolic equations ». Časopis pro pěstování matematiky 111, n^o 3 (1986) : 294–303. http://dx.doi.org/10.21136/cpm.1986.108153.

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Begtoša, Mislava, et Tvrtko Vuković. « Lov na degenerike ». Scrinia Slavonica 20, n^o 1 (15 février 2021) : 149–88. http://dx.doi.org/10.22586/ss.20.1.11.

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Polazeći od psihijatrijskog slučaja Miloša Krpana, jednog od naših prvih socijalista i anarhista, koji je koncem 19. stoljeća dva puta primljen u Kraljevski zemaljski zavod za umobolne u Stenjevcu, radom se pokušava pokazati kako onodobna psihijatrija, sudjelujući u procesu oblikovanja hrvatskog građanskog društva, osim medicinskog znanja, razvija i normalizacijsku moć. Psihijatrija pacificira otpor sustavu tako što ga izmješta u Zavod te ga ondje ispituje, obrađuje, svladava i disciplinira. Istodobno sebi pribavlja znanstveni legitimitet i stječe društveni status proizvodeći kategoriju nenormalnosti te razvijajući tehnike za njezino suzbijanje. Tako preuzima odgovornost za ćudoređe, sigurnost i čistoću društva, a povezujući se sa sudskom praksom postaje nositelj pravne moći. Drugim riječima, osim što nastoji liječiti ludilo, psihijatrija se javlja kao stroj društvene discipline uspostavljajući moderne oblike normalizacijske moći u mladom buržoazijskom kapitalističkom društvu druge polovice 19. stoljeća.

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Kufner, Alois, et Salvatore Leonardi. « Solvability of degenerate elliptic boundary value problems : another approach ». Mathematica Bohemica 119, n^o 3 (1994) : 255–74. http://dx.doi.org/10.21136/mb.1994.126167.

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Przytycki, Józef H., et Krzysztof K. Putyra. « The degenerate distributive complex is degenerate ». European Journal of Mathematics 2, n^o 4 (20 octobre 2016) : 993–1012. http://dx.doi.org/10.1007/s40879-016-0116-2.

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Duran, Ugur. « Degenerate Sumudu transform and its properties ». Filomat 35, n^o 14 (2021) : 4731–41. http://dx.doi.org/10.2298/fil2114731d.

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Kim-Kim (Russ. J. Math. Phys. 2017, 24, 241-248) defined the degenerate Laplace transform and investigated some of their certain properties. Motivated by this study, in this paper, we introduce the degenerate Sumudu transform and establish some properties and relations. We derive degenerate Sumudu transforms of power functions, degenerate sine, degenerate cosine, degenerate hyperbolic sine, degenerate hyperbolic cosine, degenerate exponential function, and function derivatives. We also acquire a relationship between degenerate Sumudu transform and degenerate gamma function. Moreover, we investigate a scale preserving theorem for the degenerate Sumudu transform. Furthermore, we show that the degenerate Sumudu transform is the theoretical dual transform to the degenerate Laplace transform.

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Kim, Hye Kyung. « Fully degenerate Bell polynomials associated with degenerate Poisson random variables ». Open Mathematics 19, n^o 1 (1 janvier 2021) : 284–96. http://dx.doi.org/10.1515/math-2021-0022.

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Abstract Many mathematicians have studied degenerate versions of quite a few special polynomials and numbers since Carlitz’s work (Utilitas Math. 15 (1979), 51–88). Recently, Kim et al. studied the degenerate gamma random variables, discrete degenerate random variables and two-variable degenerate Bell polynomials associated with Poisson degenerate central moments, etc. This paper is divided into two parts. In the first part, we introduce a new type of degenerate Bell polynomials associated with degenerate Poisson random variables with parameter α > 0 \alpha \hspace{-0.15em}\gt \hspace{-0.15em}0 , called the fully degenerate Bell polynomials. We derive some combinatorial identities for the fully degenerate Bell polynomials related to the n n th moment of the degenerate Poisson random variable, special numbers and polynomials. In the second part, we consider the fully degenerate Bell polynomials associated with degenerate Poisson random variables with two parameters α > 0 \alpha \gt 0 and β > 0 \beta \hspace{-0.15em}\gt \hspace{-0.15em}0 , called the two-variable fully degenerate Bell polynomials. We show their connection with the degenerate Poisson central moments, special numbers and polynomials.

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Zhang, Jie, Bo Tian, Qi-Xing Qu, Chen-Rong Zhang, Xia-Xia Du et Su-Su Chen. « Bound-state solitons for a non-linear Schrödinger system with the negatively coherent coupling in a weakly birefringent fiber ». Modern Physics Letters B 34, n^o 36 (10 septembre 2020) : 2050423. http://dx.doi.org/10.1142/s0217984920504230.

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In this paper, we study a non-linear Schrödinger system with the negatively coherent coupling in a weakly birefringent fiber for two orthogonally polarized optical pulses. With respect to the slowly-varying envelopes of two interacting optical modes and based on the existing binary Darboux transformation, we obtain four types of the bound-state solitons: degenerate-I, degenerate-II, degenerate–non-degenerate, and non-degenerate–non-degenerate bound-state solitons. We graphically analyze the interactions between the degenerate or non-degenerate solitons and four types of the bound-state solitons. When the degenerate solitons interact with the bound-state solitons, amplitudes and widths of the degenerate solitons remain unchanged. When the non-degenerate solitons interact with the bound-state solitons, amplitudes and widths of the bound-state solitons remain unchanged.

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Kim, Taekyun, Dae San Kim et Hye Kyung Kim. « Some identities related to degenerate Stirling numbers of the second kind ». Demonstratio Mathematica 55, n^o 1 (1 janvier 2022) : 812–21. http://dx.doi.org/10.1515/dema-2022-0170.

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Abstract The degenerate Stirling numbers of the second kind were introduced as a degenerate version of the ordinary Stirling numbers of the second kind. They appear very frequently when one studies various degenerate versions of some special numbers and polynomials. The aim of this article is to further study some identities and properties related to the degenerate Stirling numbers of the second kind, in connection with the degenerate Bell polynomials, the degenerate Fubini polynomials, the degenerate Bernoulli polynomials, and the degenerate Euler polynomials.

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Kim, T., et D. S. Kim. « Degenerate Laplace transform and degenerate gamma function ». Russian Journal of Mathematical Physics 24, n^o 2 (avril 2017) : 241–48. http://dx.doi.org/10.1134/s1061920817020091.

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Kim, Taekyun, et Dae San Kim. « Degenerate polyexponential functions and degenerate Bell polynomials ». Journal of Mathematical Analysis and Applications 487, n^o 2 (juillet 2020) : 124017. http://dx.doi.org/10.1016/j.jmaa.2020.124017.

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Chrastina, Jan. « Examples from the calculus of variations. II. A degenerate problem ». Mathematica Bohemica 125, n^o 2 (2000) : 187–97. http://dx.doi.org/10.21136/mb.2000.125951.

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Bonafede, Salvatore. « Existence results for a class of semilinear degenerate elliptic equations ». Mathematica Bohemica 128, n^o 2 (2003) : 187–98. http://dx.doi.org/10.21136/mb.2003.134032.

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Kim, Taekyun, Dae San Kim et Jin-Woo Park. « Fully degenerate Bernoulli numbers and polynomials ». Demonstratio Mathematica 55, n^o 1 (1 janvier 2022) : 604–14. http://dx.doi.org/10.1515/dema-2022-0160.

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Abstract The aim of this article is to study the fully degenerate Bernoulli polynomials and numbers, which are a degenerate version of Bernoulli polynomials and numbers and arise naturally from the Volkenborn integral of the degenerate exponential functions on Z p {{\mathbb{Z}}}_{p} . We find some explicit expressions for the fully degenerate Bernoulli polynomials and numbers in terms of the degenerate Stirling numbers of the second kind, the degenerate r r -Stirling numbers of the second kind, and the degenerate Stirling polynomials. We also consider the degenerate poly-Bernoulli polynomials and derive explicit representations for them in terms of the same degenerate Stirling numbers and polynomials.

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Kim, Byung Moon, Taekyun Kim, Jin-Woo Park et Taha Ali Radwan. « Identities on Changhee Polynomials Arising from λ -Sheffer Sequences ». Complexity 2022 (7 juin 2022) : 1–16. http://dx.doi.org/10.1155/2022/5868689.

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In this paper, authors found a new and interesting identity between Changhee polynomials and some degenerate polynomials such as degenerate Bernoulli polynomials of the first and second kind, degenerate Euler polynomials, degenerate Daehee polynomials, degenerate Bell polynomials, degenerate Lah–Bell polynomials, and degenerate Frobenius–Euler polynomials and Mittag–Leffer polynomials by using λ -Sheffer sequences and λ -differential operators to find the coefficient polynomial when expressing the n -th Changhee polynomials as a linear combination of those degenerate polynomials. In addition, authors derive the inversion formulas of these identities.

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Kim, Taekyun, Dae San Kim, Han Young Kim et Jongkyum Kwon. « Some Identities of Degenerate Bell Polynomials ». Mathematics 8, n^o 1 (1 janvier 2020) : 40. http://dx.doi.org/10.3390/math8010040.

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The new type degenerate of Bell polynomials and numbers were recently introduced, which are a degenerate version of Bell polynomials and numbers and are different from the previously introduced partially degenerate Bell polynomials and numbers. Several expressions and identities on those polynomials and numbers were obtained. In this paper, as a further investigation of the new type degenerate Bell polynomials, we derive several identities involving those degenerate Bell polynomials, Stirling numbers of the second kind and Carlitz’s degenerate Bernoulli or degenerate Euler polynomials. In addition, we obtain an identity connecting the degenerate Bell polynomials, Cauchy polynomials, Bernoulli numbers, Stirling numbers of the second kind and degenerate Stirling numbers of the second kind.

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Ma, Minyoung, et Dongkyu Lim. « Degenerate Derangement Polynomials and Numbers ». Fractal and Fractional 5, n^o 3 (22 juin 2021) : 59. http://dx.doi.org/10.3390/fractalfract5030059.

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In this paper, we consider a new type of degenerate derangement polynomial and number, which shall be called the degenerate derangement polynomials and numbers of the second kind. These concepts are motivated by Kim et al.’s work on degenerate derangement polynomials and numbers. We investigate some properties of these new degenerate derangement polynomials and numbers and explore their connections with the degenerate gamma distributions for the case λ∈(−1,0). In more detail, we derive their explicit expressions, recurrence relations, and some identities involving our degenerate derangement polynomials and numbers and other special polynomials and numbers, which include the fully degenerate Bell polynomials, the degenerate Fubini polynomials, and the degenerate Stirling numbers of the first and the second kinds. We also show that those polynomials and numbers are connected with the moments of some variants of the degenerate gamma distributions. Moreover, we compare the degenerate derangement polynomials and numbers of the second kind to those of Kim et al.

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Kemp, Walter Michael. « Presidential Address : Parasitology : A Degenerate Discipline, Populated by Degenerate Scientists, Studying Degenerate Organisms ? » Journal of Parasitology 75, n^o 6 (décembre 1989) : 817. http://dx.doi.org/10.2307/3282860.

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Kim, Hye Kyung, et Dmitry V. Dolgy. « Degenerate Catalan-Daehee numbers and polynomials of order $ r $ arising from degenerate umbral calculus ». AIMS Mathematics 7, n^o 3 (2022) : 3845–65. http://dx.doi.org/10.3934/math.2022213.

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<abstract>Many mathematicians have studied degenerate versions of some special polynomials and numbers that can take into account the surrounding environment or a person's psychological burden in recent years, and they've discovered some interesting results. Furthermore, one of the most important approaches for finding the combinatorial identities for the degenerate version of special numbers and polynomials is the umbral calculus. The Catalan numbers and the Daehee numbers play important role in connecting relationship between special numbers. In this paper, we first define the degenerate Catalan-Daehee numbers and polynomials and aim to study the relation between well-known special polynomials and degenerate Catalan-Daehee polynomials of order $ r $ as one of the generalizations of the degenerate Catalan-Daehee polynomials by using the degenerate Sheffer sequences. Some of them include the degenerate and other special polynomials and numbers such as the degenerate falling factorials, the degenerate Bernoulli polynomials and numbers of order $ r $, the degenerate Euler polynomials and numbers of order $ r $, the degenerate Daehee polynomials of order $ r $, the degenerate Bell polynomials, and so on.</abstract>

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Pyo, Sung-Soo, Taekyun Kim et Seog-Hoon Rim. « Degenerate Daehee Numbers of the Third Kind ». Mathematics 6, n^o 11 (6 novembre 2018) : 239. http://dx.doi.org/10.3390/math6110239.

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In this paper, we define new Daehee numbers, the degenerate Daehee numbers of the third kind, using the degenerate log function as generating function. We obtain some identities for the degenerate Daehee numbers of the third kind associated with the Daehee, degenerate Daehee, and degenerate Daehee numbers of the second kind. In addition, we derive a differential equation associated with the degenerate log function. We deduce some identities from the differential equation.

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Stebbins, Michael. « Degenerate mice ». Nature Medicine 8, n^o 7 (juillet 2002) : 670. http://dx.doi.org/10.1038/nm0702-670.

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van der Giezen, Mark, et Jorge Tovar. « Degenerate mitochondria ». EMBO reports 6, n^o 6 (juin 2005) : 525–30. http://dx.doi.org/10.1038/sj.embor.7400440.

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Bolotin, Sergey V. « Degenerate billiards ». Proceedings of the Steklov Institute of Mathematics 295, n^o 1 (novembre 2016) : 45–62. http://dx.doi.org/10.1134/s0081543816080046.

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Martin, Adam. « DEGENERATE COSMOPOLITANISM ». Social Philosophy and Policy 32, n^o 1 (2015) : 74–100. http://dx.doi.org/10.1017/s0265052515000084.

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Abstract:Advocates of cosmopolitan ideals, to the extent that they engage with questions of institutional design, typically imagine replicating or refining existing, nation-state models of governance but on an international scale. This essay argues that cosmopolitan ethics need not go hand in hand with international government, and may be better served by a different approach. I explore the concept of degeneracy as a principle of institutional evaluation and design in international politics. Degeneracy is a characteristic of complex systems in which multiple components of the system offer overlapping (but not identical) functions, and is a key component in the robustness of such systems. Non-degenerate systems, by contrast, exhibit fragility in the face of adverse conditions. When applied to systems of governance, degeneracy commends polycentricity and allows for some evaluation of the robustness of different mechanisms and forms of polycentric governance. Cosmopolitan ideals are better served by providing alternatives to existing forms of governance than by building on them. I consider some concrete policy applications of this idea, focusing on immigration and intellectual property.

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Floridi, Luciano. « Degenerate Epistemology ». Philosophy & ; Technology 25, n^o 1 (10 février 2012) : 1–3. http://dx.doi.org/10.1007/s13347-012-0067-6.

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Scharff Smith, Peter. « “Degenerate Criminals” ». Criminal Justice and Behavior 35, n^o 8 (août 2008) : 1048–64. http://dx.doi.org/10.1177/0093854808318782.

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Inspired by the breakthrough of the discipline of criminology and biological theories of degeneration, prison psychiatry became a flourishing field during the latter decades of the 19th century. This is reflected in the history of the Vridsløselille penitentiary in Denmark, which operated as a Pennsylvania-model institution with strict solitary confinement from 1859 to the early 1930s. Throughout the period, this prison experienced extensive problems with inmate mental health, and as the discipline of psychiatry developed, mental disorders were given new names and old diseases disappeared. Although prison authorities were willing to acknowledge the damaging effects of the isolation regimes being employed, a number of psychiatrists located the causes of mental disorders among biological dispositional traits rather than situational factors. In doing so, they downplayed the power of the prison context and offered biological “degeneration” among criminals as an alternative explanation.

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Font, A., L. E. Ibáñez, H. P. Nilles et F. Quevedo. « Degenerate orbifolds ». Nuclear Physics B 307, n^o 1 (septembre 1988) : 109–29. http://dx.doi.org/10.1016/0550-3213(88)90524-x.

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Burton, Adrian. « Degenerate diners ». Frontiers in Ecology and the Environment 16, n^o 3 (avril 2018) : 192. http://dx.doi.org/10.1002/fee.1790.

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Kim, Taekyun, Dae San Kim et Hye Kyung Kim. « Degenerate r -Bell Polynomials Arising from Degenerate Normal Ordering ». Journal of Mathematics 2022 (12 octobre 2022) : 1–6. http://dx.doi.org/10.1155/2022/2626249.

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Recently, Kim-Kim introduced the degenerate r -Bell polynomials and investigated some results which are derived from umbral calculus. The aim of this paper is to study some properties of the degenerate r -Bell polynomials and numbers via boson operators. In particular, we obtain two expressions for the generating function of the degenerate r -Bell polynomials in z 2 , and a recurrence relation and Dobinski-like formula for the degenerate r -Bell numbers. These are derived from the degenerate normal ordering of a degenerate integral power of the number operator in terms of boson operators where the degenerate r -Stirling numbers of the second kind appear as the coefficients.

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Kim, Dojin, Patcharee Wongsason et Jongkyum Kwon. « Type 2 degenerate modified poly-Bernoulli polynomials arising from the degenerate poly-exponential functions ». AIMS Mathematics 7, n^o 6 (2022) : 9716–30. http://dx.doi.org/10.3934/math.2022541.

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<abstract>We present a new type of degenerate poly-Bernoulli polynomials and numbers by modifying the polyexponential function in terms of the degenerate exponential functions and degenerate logarithm functions. Also, we introduce a new variation of the degenerate unipoly-Bernoulli polynomials by the similar modification. Based on these polynomials, we investigate some properties, new identities, and their relations to the known special functions and numbers such as the degenerate type 2-Bernoulli polynomials, the type 2 degenerate Euler polynomials, the degenerate Bernoulli polynomials and numbers, the degenerate Stirling numbers of the first kind, and $ \lambda $-falling factorial sequence. In addition, we compute some of the proposed polynomials and present their zeros and behaviors for different variables in specific cases.</abstract>

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Kim, Taekyun, Dae San Kim, Dmitry V. Dolgy et Jin-Woo Park. « Degenerate binomial and Poisson random variables associated with degenerate Lah-Bell polynomials ». Open Mathematics 19, n^o 1 (1 janvier 2021) : 1588–97. http://dx.doi.org/10.1515/math-2021-0116.

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Abstract The aim of this paper is to study the Poisson random variables in relation to the Lah-Bell polynomials and the degenerate binomial and degenerate Poisson random variables in connection with the degenerate Lah-Bell polynomials. Among other things, we show that the rising factorial moments of the degenerate Poisson random variable with parameter α \alpha are given by the degenerate Lah-Bell polynomials evaluated at α \alpha . We also show that the probability-generating function of the degenerate Poisson random variable is equal to the generating function of the degenerate Lah-Bell polynomials. Also, we show similar results for the Poisson random variables. Here the n n th Lah-Bell number counts the number of ways a set of n n elements can be partitioned into non-empty linearly ordered subsets, the Lah-Bell polynomials are natural extensions of the Lah-Bell numbers and the degenerate Lah-Bell polynomials are degenerate versions of the Lah-Bell polynomials.

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Kim, T., et D. S. Kim. « On Some Degenerate Differential and Degenerate Difference Operators ». Russian Journal of Mathematical Physics 29, n^o 1 (mars 2022) : 37–46. http://dx.doi.org/10.1134/s1061920822010046.

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Hausrath, Alan R., et Raul F. Manasevich. « The characterization of degenerate and non-degenerate systems ». Rocky Mountain Journal of Mathematics 16, n^o 1 (mars 1986) : 203–14. http://dx.doi.org/10.1216/rmj-1986-16-1-203.

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Maxted, Pierre F. L., Luisa Morales-Rueda et Tom R. Marsh. « Companions to sdB binaries-degenerate or non-degenerate ? » Astrophysics and Space Science 291, n^o 3 (2004) : 307–14. http://dx.doi.org/10.1023/b:astr.0000044337.19671.de.

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Alon, Noga. « A Note on Degenerate and Spectrally Degenerate Graphs ». Journal of Graph Theory 72, n^o 1 (1 mai 2012) : 1–6. http://dx.doi.org/10.1002/jgt.21627.

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Khan, Waseem A., Rifaqat Ali, Khaled Ahmad Hassan Alzobydi et Naeem Ahmed. « A New Family of Degenerate Poly-Genocchi Polynomials with Its Certain Properties ». Journal of Function Spaces 2021 (9 juin 2021) : 1–8. http://dx.doi.org/10.1155/2021/6660517.

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In this paper, we introduce a new type of degenerate Genocchi polynomials and numbers, which are called degenerate poly-Genocchi polynomials and numbers, by using the degenerate polylogarithm function, and we derive several properties of these polynomials systematically. Then, we also consider the degenerate unipoly-Genocchi polynomials attached to an arithmetic function, by using the degenerate polylogarithm function, and investigate some identities of those polynomials. In particular, we give some new explicit expressions and identities of degenerate unipoly polynomials related to special numbers and polynomials.

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Komatsu, Takao. « Two types of hypergeometric degenerate Cauchy numbers ». Open Mathematics 18, n^o 1 (29 mai 2020) : 417–33. http://dx.doi.org/10.1515/math-2020-0030.

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Abstract In 1985, Howard introduced degenerate Cauchy polynomials together with degenerate Bernoulli polynomials. His degenerate Bernoulli polynomials have been studied by many authors, but his degenerate Cauchy polynomials have been forgotten. In this paper, we introduce some kinds of hypergeometric degenerate Cauchy numbers and polynomials from the different viewpoints. By studying the properties of the first one, we give their expressions and determine the coefficients. Concerning the second one, called H-degenerate Cauchy polynomials, we show several identities and study zeta functions interpolating these polynomials.

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Kim, Taekyun, et Hye Kyung Kim. « Degenerate Poly-Lah-Bell Polynomials and Numbers ». Journal of Mathematics 2022 (25 février 2022) : 1–9. http://dx.doi.org/10.1155/2022/2917943.

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Many mathematicians studied “poly” as a generalization of the well-known special polynomials such as Bernoulli polynomials, Euler polynomials, Cauchy polynomials, and Genocchi polynomials. In this paper, we define the degenerate poly-Lah-Bell polynomials arising from the degenerate polyexponential functions which are reduced to degenerate Lah-Bell polynomials when k = 1 . In particular, we call these polynomials the “poly-Lah-Bell polynomials” when λ ⟶ 0 . We give their explicit expression, Dobinski-like formulas, and recurrence relation. In addition, we obtain various algebraic identities including Lah numbers, the degenerate Stirling numbers of the first and second kind, the degenerate poly-Bell polynomials, the degenerate poly-Bernoulli numbers, and the degenerate poly-Genocchi numbers.

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Tleubergenov, M. I., et G. T. Ibraeva. « ON INVERSE PROBLEM OF CLOSURE OF DIFFERENTIAL SYSTEMS WITH DEGENERATE DIFFUSION ». Eurasian Mathematical Journal 10, n^o 2 (2019) : 93–102. http://dx.doi.org/10.32523/2077-9879-2019-10-2-93-102.

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Vavrukh, M., D. Dzikovskyi, V. Solovyan et N. Tyshko. « Correlation functions of the degenerate relativistic electron gas with high density ». Mathematical Modeling and Computing 3, n^o 1 (1 juillet 2016) : 97–110. http://dx.doi.org/10.23939/mmc2016.01.097.

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Vavrukh, M., S. Smerechynskyi et D. Dzikovskyi. « The influence of the axial rotation on the degenerate dwarfs characteristics ». Mathematical Modeling and Computing 4, n^o 1 (1 juillet 2017) : 107–15. http://dx.doi.org/10.23939/mmc2017.01.107.

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Hwang, Kyung-Won, et Cheon Seoung Ryoo. « Differential Equations Associated with Two Variable Degenerate Hermite Polynomials ». Mathematics 8, n^o 2 (10 février 2020) : 228. http://dx.doi.org/10.3390/math8020228.

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In this paper, we introduce the two variable degenerate Hermite polynomials and obtain some new symmetric identities for two variable degenerate Hermite polynomials. In order to give explicit identities for two variable degenerate Hermite polynomials, differential equations arising from the generating functions of degenerate Hermite polynomials are studied. Finally, we investigate the structure and symmetry of the zeros of the two variable degenerate Hermite equations.

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Kim, YunJae, Byung Kim, Lee-Chae Jang et Jongkyum Kwon. « A Note on Modified Degenerate Gamma and Laplace Transformation ». Symmetry 10, n^o 10 (10 octobre 2018) : 471. http://dx.doi.org/10.3390/sym10100471.

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Kim-Kim studied some properties of the degenerate gamma and degenerate Laplace transformation and obtained their properties. In this paper, we define modified degenerate gamma and modified degenerate Laplace transformation and investigate some properties and formulas related to them.

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47

Kim, Dojin, et Sangil Kim. « Properties of Partially Degenerate Complex Appell Polynomials ». Symmetry 11, n^o 12 (11 décembre 2019) : 1508. http://dx.doi.org/10.3390/sym11121508.

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Degenerate versions of polynomial sequences have been recently studied to obtain useful properties such as symmetric identities by introducing degenerate exponential-type generating functions. As part of our continued work in degenerate versions of generating functions, we subsequently present our study on degenerate complex Appell polynomials by considering a partially degenerate version of the generating functions of ordinary complex Appell polynomials in this paper. We only consider partially degenerate generating functions to retain the crucial properties of the Appell sequence, and we present useful identities and general properties by splitting complex values into their real and imaginary parts; moreover, we provide several explicit examples. Additionally, the differential equations satisfied by degenerate complex Bernoulli and Euler polynomials are derived by the quasi-monomiality principle using Appell-type polynomials.

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48

Kim, Taekyun, Lee-Chae Jang, Dae San Kim et Han Young Kim. « Some Identities on Type 2 Degenerate Bernoulli Polynomials of the Second Kind ». Symmetry 12, n^o 4 (2 avril 2020) : 510. http://dx.doi.org/10.3390/sym12040510.

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In recent years, many mathematicians studied various degenerate versions of some special polynomials for which quite a few interesting results were discovered. In this paper, we introduce the type 2 degenerate Bernoulli polynomials of the second kind and their higher-order analogues, and study some identities and expressions for these polynomials. Specifically, we obtain a relation between the type 2 degenerate Bernoulli polynomials of the second and the degenerate Bernoulli polynomials of the second, an identity involving higher-order analogues of those polynomials and the degenerate Stirling numbers of the second kind, and an expression of higher-order analogues of those polynomials in terms of the higher-order type 2 degenerate Bernoulli polynomials and the degenerate Stirling numbers of the first kind.

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49

He, Fuli, Ahmed Bakhet, Mohamed Akel et Mohamed Abdalla. « Degenerate Analogues of Euler Zeta, Digamma, and Polygamma Functions ». Mathematical Problems in Engineering 2020 (6 mai 2020) : 1–9. http://dx.doi.org/10.1155/2020/8614841.

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In recent years, much attention has been paid to the role of degenerate versions of special functions and polynomials in mathematical physics and engineering. In the present paper, we introduce a degenerate Euler zeta function, a degenerate digamma function, and a degenerate polygamma function. We present several properties, recurrence relations, infinite series, and integral representations for these functions. Furthermore, we establish identities involving hypergeometric functions in terms of degenerate digamma function.

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50

Hwang, Kyung-Won, et Cheon Seoung Ryoo. « Some Identities Involving Two-Variable Partially Degenerate Hermite Polynomials Induced from Differential Equations and Structure of Their Roots ». Mathematics 8, n^o 4 (20 avril 2020) : 632. http://dx.doi.org/10.3390/math8040632.

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In this paper, we introduce two-variable partially degenerate Hermite polynomials and get some new symmetric identities for two-variable partially degenerate Hermite polynomials. We study differential equations induced from the generating functions of two-variable partially degenerate Hermite polynomials to give identities for two-variable partially degenerate Hermite polynomials. Finally, we study the symmetric properties of the structure of the roots of the two-variable partially degenerate Hermite equations.

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