41 results
Search Results
2. The heat kernel of sub-Laplace operator on nilpotent Lie groups of step two.
- Author
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Chang, Der-Chen, Kang, Qianqian, and Wang, Wei
- Subjects
HAMILTON-Jacobi equations ,NILPOTENT Lie groups ,MATHEMATICAL physics ,DIFFERENTIAL operators ,MATHEMATICAL analysis ,FOURIER analysis ,MATHEMATICS - Abstract
The Laguerre calculus is widely used for the inversion of differential operators on the Heisenberg group. Applying the Laguerre calculus established on nilpotent Lie groups of step two in Chang et al. [The Laguerre calculus on the nilpotent Lie group of step two. Preprint; 2019. Available from: ], we find the explicit formulas for the heat kernel of sub-Laplace operator and the fundamental solution of power of sub-Laplace operator on nilpotent Lie groups of step two. Calin, Chang and Markina [Generalized Hamilton–Jacobi equation and heat kernel on step two nilpotent Lie groups. In: Gustafsson B, Vasil'ev A, editors. Analysis and mathematical physics. Basel: Birkhüser; 2009 (Trends in mathematics)] also get the formulas for the heat kernel of sub-Laplace operator on nilpotent Lie groups of step two by using the Hamiltonian and Lagrangian formalisms that are related to geometric mechanics. In this paper, we use a totally different method to prove our main results by using the Laguerre calculus, which is more direct from the point of view of Fourier analysis. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
3. Empirical Likelihood in Causal Inference.
- Author
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Zhang, Biao
- Subjects
PROBABILITY theory ,MATHEMATICAL functions ,MATHEMATICS ,DIFFERENTIAL equations ,MATHEMATICAL analysis - Abstract
This paper discusses the estimation of average treatment effects in observational causal inferences. By employing a working propensity score and two working regression models for treatment and control groups, Robins et al. (1994, 1995) introduced the augmented inverse probability weighting (AIPW) method for estimation of average treatment effects, which extends the inverse probability weighting (IPW) method of Horvitz and Thompson (1952); the AIPW estimators are locally efficient and doubly robust. In this paper, we study a hybrid of the empirical likelihood method and the method of moments by employing three estimating functions, which can generate estimators for average treatment effects that are locally efficient and doubly robust. The proposed estimators of average treatment effects are efficient for the given choice of three estimating functions when the working propensity score is correctly specified, and thus are more efficient than the AIPW estimators. In addition, we consider a regression method for estimation of the average treatment effects when working regression models for both the treatment and control groups are correctly specified; the asymptotic variance of the resulting estimator is no greater than the semiparametric variance bound characterized by the theory of Robins et al. (1994, 1995). Finally, we present a simulation study to compare the finite-sample performance of various methods with respect to bias, efficiency, and robustness to model misspecification. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
4. Extension of analytic covers by extension of their ramification divisors.
- Author
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Lavoine, L.
- Subjects
EXTENSION (Logic) ,DIVISOR theory ,MATHEMATICAL proofs ,MATHEMATICAL analysis ,MATHEMATICS - Abstract
This paper deals with extension of analytic covers. We prove topological extension theorems for analytic covers. The main result is an extension theorem which only uses the extension of the ramification divisor. We give also a Thullen-type and a Hartogs-type extensions theorems. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
5. Some remarks about monoidal Hom-algebras.
- Author
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Alonso Álvarez, J.N., Fernández Vilaboa, J.M., and González Rodríguez, R.
- Subjects
ALGEBRA ,MATHEMATICS ,MATHEMATICAL analysis ,TENSOR products ,CALCULUS of tensors - Abstract
In this paper, for 𝒞 a strict braided monoidal category with tensor product ⊗, we improve the definition of Hom-associative algebra by removing the multiplicativity condition of the automorphismα. After that we state the close connection between the classical notions of (co)algebra, (co)module and Hopf algebra and the corresponding ones in the Hom-world. As a consequence we can study the questions about the Hom-world by passing to the classical one, and the main contribution of this paper is to illustrate the suitable procedure to move from one side to the other. Finally, we apply our techniques to get in the Hom setting some classical results about cleft and Galois extensions. [ABSTRACT FROM PUBLISHER]
- Published
- 2017
- Full Text
- View/download PDF
6. A three-population constrained discrimination procedure.
- Author
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Patterson, David
- Subjects
PROBABILITY theory ,MATHEMATICAL optimization ,MATHEMATICAL analysis ,MATHEMATICS ,SIMULATION methods & models - Abstract
Classification rules with a reserve judgment option provide a way to satisfy constraints on the misclassification probabilities when there is a high degree of overlap among the populations. Constructing rules which maximize the probability of correct classification while satisfying such constraints is a difficult optimization problem. This paper uses the form of the optimal solution to develop a relatively simple and computationally fast method for three populations which has a non parametric quality in controlling the misclassification probabilities. Simulations demonstrate that this procedure performs well. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
7. Linear preservers of even majorization on M n,m.
- Author
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Soleymani, M. and Armandnejad, A.
- Subjects
STOCHASTIC matrices ,LINEAR systems ,PERMUTATIONS ,MATHEMATICS ,MATHEMATICAL analysis - Abstract
Letbe the algebra of allreal matrices. Anreal matrixis even doubly stochastic if it is a convex combination of even permutation matrices. For,is said to be even majorized by(written as), if there exists an even doubly stochastic matrixsuch that. In this paper, the concept of even majorization is investigated and then the linear preservers and strong linear preservers of this concept are characterized on. [ABSTRACT FROM PUBLISHER]
- Published
- 2014
- Full Text
- View/download PDF
8. Principal invariant subspaces theorems.
- Author
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Xu, Xiao-Ming, Fang, Xiaochun, and Gao, Fugen
- Subjects
INVARIANT subspaces ,TOPOLOGICAL spaces ,PROOF theory ,FUNCTIONAL analysis ,MATHEMATICS ,MATHEMATICAL analysis - Abstract
In this paper, we present the necessary and sufficient conditions for which the given pair of closed subspaces has a pair of non-trivial principal invariant subspaces. Using this we show that every pairof closed subspaces withorhas a pair of non-trivial principal invariant subspaces. Also we prove that the pairof closed subspaces withhas a pair of non-trivial principal invariant subspaces if and only ifSimilar results are proved for non-degenerate principal invariant subspaces. [ABSTRACT FROM PUBLISHER]
- Published
- 2014
- Full Text
- View/download PDF
9. Improving Schwarz inequality in inner product spaces.
- Author
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Dragomir, Silvestru Sever
- Subjects
MATHEMATICAL analysis ,INNER product spaces ,INNER product ,SCHWARZ function ,MATHEMATICS - Abstract
Some improvements of the celebrated Schwarz inequality in complex inner product spaces are given. Applications for n-tuples of complex numbers are provided. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
10. ON PREFERENTIAL SYLOW FUZZY SUBGROUPS.
- Author
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MAKAMBA, B. B. and MURALI, V.
- Subjects
FUZZY control systems ,MATHEMATICAL analysis ,FINITE groups ,MATHEMATICS ,POLYNOMIALS - Abstract
In this paper, for a prime p, we propose some plausible definitions for the notion of Sylow fuzzy p-subgroup of a finite group. We derive a number of results for finite fuzzy groups using one of the proposed definitions. We also discuss some of the relationships between various proposed definitions for suitability, including the crisp case, with some examples. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
11. Generalized Infinite Products for Powers of e1/k.
- Author
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Ginebaugh, Scott
- Subjects
- *
INFINITE products , *INFINITY (Mathematics) , *MATHEMATICAL analysis , *INFINITE processes , *MATHEMATICS - Abstract
Catalan and Pippenger discovered infinite products for various values related to e. Based on these, infinite products for e1/2 and e2/3 were found by Sondow and Yi [3], who furthermore conjectured that the products could be generalized for a power of e1/k . The discoveries in this paper result from attempting to prove this conjecture. By generalizing Sondow and Yi's products, infinite products for powers of e1/k are found. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
12. Extensions of BCK-algebras.
- Author
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Radfar, A., Rezaei, A., Borumand Saeid, A., and Liu, Lishan
- Subjects
- *
ALGEBRA , *MATHEMATICS , *MATHEMATICAL analysis , *ALGORITHMS , *MATHEMATICAL statistics - Abstract
In this paper, we introduce the notion of sBCI/sBCK/eBCI/eBCK-algebras as a generalization of the notion of BCI/BCK-algebras. This structure is studied in detail. Also we introduce a way to make an eBCK-algebra from a BCK-algebra and vice versa. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
13. Bayesian index to compare assumed survival functions of two hazards following exponential distributions.
- Author
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Kawasaki, Yohei, Doi, Masaaki, Ide, Kazuki, Miyaoka, Etsuo, and Shiraishi, Hiroshi
- Subjects
- *
SURVIVAL analysis (Biometry) , *BAYESIAN analysis , *PROBABILITY theory , *MATHEMATICAL analysis , *MATHEMATICS - Abstract
In clinical studies, the period before an event occurs is frequently considered as an outcome. The general term used for this analytical method in clinical studies is "survival time analysis". The method employs Cox regression to compare hazards between groups. In this paper, we propose an index defined in the Bayesian framework to compare hazards. This index compares the sizes of the hazards directly. Further, we propose two methods to calculate the sizes of the hazards. One is an approximate method, by which we can easily calculate the size, and the other is an exact method. In addition, we apply the proposed index to two actual clinical studies to assess its usability. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
14. Logarithmically complete monotonicity of Catalan-Qi function related to Catalan numbers.
- Author
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Qi, Feng, Guo, Bai-Ni, and Liu, Lishan
- Subjects
- *
MATHEMATICAL functions , *MATHEMATICAL analysis , *MATHEMATICS , *CATALAN numbers , *COMBINATORICS - Abstract
In the paper, the authors find the logarithmically complete monotonicity of the Catalan-Qi function related to the Catalan numbers. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
15. On the (In)Dependence of the Peano Axioms for Natural Numbers.
- Author
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Cerioli, Márcia R., Nobrega, Hugo, Silveira, Guilherme, and Viana, Petrucio
- Subjects
NATURAL numbers ,PEANO axioms ,ALGEBRA ,MATHEMATICAL analysis ,MATHEMATICS - Abstract
We investigate two notions of independence—(usual) independence and complete independence—applied to the Peano axioms for the sequence of natural numbers. We review the results that, although they are independent, the Peano axioms are not completely independent. The standard proof that the Peano axioms are not completely independent is algebraic, in the sense that it makes essential reference to the relationship between several mathematical structures that satisfy, or do not satisfy, these axioms. We then present an alternative logical proof, which makes no essential references to the relationship between mathematical structures. There is a completely independent set of axioms for the sequence of natural numbers, but it is based on primitives different from those originally adopted by Peano. Therefore, we present a new completely independent set of axioms based on the same set of primitives as the one originally adopted by Peano. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
16. "The moral arithmetic": morality in the age of mathematics.
- Author
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Levy-Eichel, Mordechai
- Subjects
INTELLECTUAL history ,HISTORY of mathematics ,ARITHMETIC ,HISTORY of science ,MATHEMATICAL analysis ,MATHEMATICS - Abstract
This article examines the influence of mathematics on early modern and modern moral thought. In particular, I trace the origin and development of the "moral arithmetic" (which has previously been misattributed); that is, the attempt to introduce quantificatory calculation to morality. Tracing the origins and development of both the term and the idea, I show that it was coined by the Third Earl of Shaftesbury in the seventeenth century, and that it contributed to the rise of rationalistic, utilitarian Benthamite thought in the nineteenth century, laying the foundations for the modern discipline of mathematical economics. In particular, I emphasize that, while today we habitually associate ideas of self-interest with "cold, hard" mathematical analyses, the original application of mathematics to moral thought began among the theologians and philosophers of the seventeenth and eighteenth centuries in order to combat ideas of self-interest. I conclude by reflecting on some of the problems with the scope and limits of the history of political thought, and argue for the importance of drawing intellectual history and the history of science, in particular the history of mathematics, closer together. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
17. Numerical treatment of a quasilinear initial value problem with boundary layer
- Author
-
Ilhame Amirali, Musa Cakir, Gabil M. Amiraliyev, and Erkan Cimen
- Subjects
Singular perturbation ,Logarithm ,uniformly convergence ,Applied Mathematics ,Mathematical analysis ,Perturbation (astronomy) ,Shishkin mesh ,initial layer ,010103 numerical & computational mathematics ,01 natural sciences ,Computer Science Applications ,010101 applied mathematics ,Boundary layer ,Computational Theory and Mathematics ,Error analysis ,Norm (mathematics) ,Piecewise ,Initial value problem ,0101 mathematics ,exponentially fitted difference scheme ,singular perturbation ,Mathematics - Abstract
The paper deals with the singularly perturbed quasilinear initial value problem exhibiting initial layer. First the nature of solution of differential problem before presenting method for its numerical solution is discussed. The numerical solution of the problem is performed with the use of a finite-fitted difference scheme on an appropriate piecewise uniform mesh (Shishkin-type mesh). An error analysis shows that the method is first-order convergent except for a logarithmic factor, in the discrete maximum norm, independently of the perturbation parameter. Finally, numerical results supporting the theory are presented. The paper deals with the singularly perturbed quasilinear initial value problem exhibiting initial layer. First the nature of solution of differential problem before presenting method for its numerical solution is discussed. The numerical solution of the problem is performed with the use of a finite-fitted difference scheme on an appropriate piecewise uniform mesh (Shishkin-type mesh). An error analysis shows that the method is first-order convergent except for a logarithmic factor, in the discrete maximum norm, independently of the perturbation parameter. Finally, numerical results supporting the theory are presented.
- Published
- 2016
18. Representations of Bihom-Lie superalgebras.
- Author
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Li, Juan, Chen, Liangyun, and Cheng, Yongsheng
- Subjects
MATHEMATICS ,SUPERALGEBRAS ,LIE algebras ,MATHEMATICAL analysis ,LIE groups - Abstract
The purpose of this article is to study cohomology and representations of Bihom-Lie superalgebras. In particular, trivial representations and adjoint representations of Bihom-Lie superalgebras are studied in detail. Derivations and central extensions of Bihom-Lie superalgebras are also discussed as an application. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
19. Matrices over a commutative ring as sums of three idempotents or three involutions.
- Author
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Tang, Gaohua, Zhou, Yiqiang, and Su, Huadong
- Subjects
MATHEMATICS ,MATHEMATICAL research ,MATHEMATICAL analysis ,COMMUTATIVE rings ,IDEMPOTENTS - Abstract
Motivated by Hirano-Tominaga's work on rings for which every element is a sum of two idempotents and by de Seguins Pazzis's results on decomposing every matrix over a field of positive characteristic as a sum of idempotent matrices, we address decomposing every matrix over a commutative ring as a sum of three idempotent matrices and, respectively, as a sum of three involutive matrices. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
20. Designing Mathematical Thinking Tasks.
- Author
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Breen, Sinéad and O'Shea, Ann
- Subjects
STUDENTS ,LEARNING ,MATHEMATICS ,CALCULUS ,MATHEMATICAL analysis - Abstract
Research has shown that the types of tasks assigned to students affect their learning. Various authors have described desirable features of mathematical tasks or of the activity they initiate. Others have suggested task taxonomies that might be used in classifying mathematical tasks. Drawing on this literature, we propose a set of task types that are deemed appropriate for undergraduate students and which foster mathematical habits of mind. These are: generating examples; analyzing reasoning; evaluating mathematical statements; conjecturing and/or generalizing; visualizing; and using definitions. We give rationales for our choices and examples of each type of task suitable for use in an introductory calculus course. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
21. A note on rings with McCoy-like properties.
- Author
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Habibi, M., Moussavi, A., and Šter, J.
- Subjects
RING theory ,QUOTIENT rings ,POLYNOMIAL rings ,MATHEMATICS ,MATHEMATICAL analysis - Abstract
According to Nielsen [10], a ringRis calledright McCoyif for every nonzerof(x),g(x) in the polynomial ringR[x],f(x)g(x) = 0 implies that there exists a nonzerosinRsuch thatf(x)s = 0. In this work, we state two notes on rings with McCoy-like conditions. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
22. Involution satisfying a local Engel or power commuting condition.
- Author
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Chacron, M.
- Subjects
PI-algebras ,NATURAL numbers ,RING theory ,MATHEMATICS ,MATHEMATICAL analysis - Abstract
We are given a semiprime PI-ringR(i.e.Rsatisfies some polynomial identity) with *. It is to be shown that the following conditions are equivalent. Condition 1: Each elementxofRis normal (i.e.). Condition 2: Associated to each elementxofRis a natural numberN = N(x) depending onxsuch thatwheredxmaps each elementyofRonto [y,x]( = yx−xy) andis theNth power ofdx(under composition). Condition 3: * Associated to each elementxofRis a natural numberdepending onxsuch that. [ABSTRACT FROM PUBLISHER]
- Published
- 2017
- Full Text
- View/download PDF
23. Learners' Approaches to Solving Mathematical Tasks: Does Specialisation Matter?
- Author
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Machaba, France and Mwakapenda, Willy
- Subjects
PROBLEM solving ,MATHEMATICAL analysis ,MATHEMATICS education ,MATHEMATICAL literacy ,DEVELOPMENTAL tasks - Abstract
This article emerged from an analysis of learners’ responses to a task presented to learners studying Mathematics and Mathematical Literacy (ML) in Gauteng, South Africa. Officially, Mathematics and ML are two separate learning areas. Learners from Grade 10 onwards are supposed to take either one or the other, but not both. This means that by Grade 11, learners would have acquired different kinds of knowledge and problem solving skills depending on which of these they take. The article demonstrates that this possibility may not necessarily happen. Grade 11 learners from both learning areas appeared to have acquired sufficient knowledge and skills and were able to solve similar Mathematics tasks in similar ways, with similar adequacy. We argue that, contrary to common perceptions in the field of Mathematics education (particularly in South Africa), engaging in ML does not and should not make one less mathematically advanced than engagement in pure Mathematics. [ABSTRACT FROM PUBLISHER]
- Published
- 2016
- Full Text
- View/download PDF
24. A Tale of Three Theorems.
- Author
-
Zalcman, Lawrence
- Subjects
MATHEMATICS theorems ,MATHEMATICAL functions ,MATHEMATICAL analysis ,MATHEMATICS - Abstract
This article presents a bird's eye view of the celebrated theorems of Picard and their close relatives, with particular emphasis on some surprising developments of the past half century. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
25. The Bahadur representation of sample quantiles for weakly dependent sequences.
- Author
-
Wang, Yiwei, Yang, Wenzhi, and Hu, Shuhe
- Subjects
BAHADUR representation ,QUANTILES ,MATHEMATICAL sequences ,MATHEMATICAL analysis ,MATHEMATICS - Abstract
Under some weak conditions, we use the moment inequality for-mixing sequence to investigate the Bahadur representation of sample quantiles based on this stochastic sequence. For all, we obtain a rate of Bahadur representation in the form of, which is close to the rate. [ABSTRACT FROM PUBLISHER]
- Published
- 2016
- Full Text
- View/download PDF
26. The Exchange Property in Grothendieck Categories: Applications.
- Author
-
Dăuş, L., Năstăsescu, C., and Salim, M.
- Subjects
GROTHENDIECK categories ,MODULES (Algebra) ,RING theory ,MATHEMATICS ,MATHEMATICAL analysis - Abstract
We introduce the concept of an object with the (finite) exchange property in an arbitrary Grothendieck category, and we present the basic properties of such an object. Applications are given for categories of graded modules and for categories of comodules over a coalgebra. Among other results, it is proved that an arbitrary coalgebra 𝒞 over a field has the finite exchange property. [ABSTRACT FROM PUBLISHER]
- Published
- 2016
- Full Text
- View/download PDF
27. Matrix completion and tensor rank.
- Author
-
Derksen, Harm
- Subjects
TENSOR algebra ,MATRICES (Mathematics) ,PROBLEM solving ,MATHEMATICS ,MATHEMATICAL analysis - Abstract
We show that the low rank matrix completion problem can be reduced to the problem of finding the rank of a certain tensor. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
28. Comment: Some Enhancements Over the Augmented Lagrangian Approach.
- Author
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Picheny, Victor, Ginsbourger, David, and Krityakierne, Tipaluck
- Subjects
CONSTRAINED optimization ,MATHEMATICAL optimization ,MATHEMATICAL analysis ,MATHEMATICS ,MATHEMATICAL formulas - Abstract
The article reviews the main situations one may encounter in constrained optimization of computer experiments, some of the corresponding existing tools and areas open for innovation. Topics discussed include the analytical formulas of the main criterion of L. Gramacy et al for the single constraint problem and the general behavior of the AL strategy and proposed modifications to improve its efficiency.
- Published
- 2016
- Full Text
- View/download PDF
29. ON THE CONGRUENCES IN RIGHT LOOPS.
- Author
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Kakkar, Vipul and Shukla, R.P.
- Subjects
GEOMETRIC congruences ,LOOPS (Group theory) ,STABILITY theory ,MATHEMATICS ,MATHEMATICAL analysis - Abstract
In case the stability relation is a congruence, a necessary and also a sufficient condition for its equality with the center congruence is given. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
30. ON THE WITT VECTORS OF PERFECT RINGS IN POSITIVE CHARACTERISTIC.
- Author
-
Shimomoto, Kazuma
- Subjects
VECTOR algebra ,RING theory ,FROBENIUS algebras ,MATHEMATICAL mappings ,MATHEMATICS ,MATHEMATICAL analysis - Abstract
The purpose of this article is to prove some results on the Witt vectors of perfect F
p -algebras. Let A be a perfect Fp -algebra for a prime integer p, and assume that A has the property P. Then does the ring of Witt vectors of A also have P A main theorem gives an affirmative answer for P =integrally closed" under a very mild condition. [ABSTRACT FROM AUTHOR]- Published
- 2015
- Full Text
- View/download PDF
31. ON THE PURE-INJECTIVITY PROFILE OF A RING.
- Author
-
Harmanci, Abdullah, López-Permouth, SergioR., and Ungor, Burcu
- Subjects
INJECTIVE functions ,RING theory ,MODULES (Algebra) ,MATHEMATICS ,MATHEMATICAL analysis - Abstract
An analog of the injective profile of a ring, with relative injectivity replaced by relative pure-injeetivity, is investigated. Emphasis is placed on comparing and contrasting the properties of hot h profiles. In particular, the analog in this context of the notion of poor modules is considered and properties of pure-injeetively poor modules are determined. While we do not know of any ring that does not have pure-injectively poor modules, their existence has not been determined in general. Rings having pure-injectively poor modules of various types are characterized. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
32. ON B(n, k) 2-GROUPS.
- Author
-
Wang, Huiqun, Tan, Yilan, and Moss, Tyson
- Subjects
FINITE groups ,GROUP theory ,SET theory ,MATHEMATICS ,MATHEMATICAL analysis - Abstract
A finite group G is said to he a B(n, k) group if for any n-element subset {a
1 ,...,an } of G, |{ai aj |1≥ i, j ≥ n}| ≥ k. In this article, we give characterizations of the B(5, 19) 2-groups, and the 11(6, k) 2-groups for 21 ≥ k ≥ 28. [ABSTRACT FROM AUTHOR]- Published
- 2015
- Full Text
- View/download PDF
33. Numerical Analyses on the Adhesive Contact between a Sphere and a Longitudinal Wavy Surface.
- Author
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Wu, Jiunn-Jong and Lin, Yu Ju
- Subjects
ADHESIVES ,ADHESION ,NUMERICAL analysis ,MATHEMATICAL analysis ,MATHEMATICS - Abstract
The adhesive contact between a sphere and a longitudinal wavy surface is simulated numerically. A modified simulation method is proposed using the Newton BI-CGSTAB method in a rectangular coordinate. The effective Tabor parameter is proposed. It is found that when the amplitude of the wavy surface is larger, the contact area is smaller and the pull-off force is smaller. Jump-in from noncontact phenomena occurs when the Tabor parameter is large. Jumping from one ridge to the next ridge occurs when the effect of the Tabor parameter is large and the amplitude of the wavy surface is not too small. Jumping from noncontact to full contact is affected by the amplitude and the wave number of the wavy surface and is also affected by the Tabor parameter. [ABSTRACT FROM PUBLISHER]
- Published
- 2015
- Full Text
- View/download PDF
34. Characteristics of number transcoding errors of Chinese- versus English-speaking Alzheimer's disease patients.
- Author
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Ting, Simon Kang Seng, Chia, Pei Shi, Kwek, Kevin, Tan, Wilnard, and Hameed, Shahul
- Subjects
ENGLISH as a foreign language ,TRANSCODING ,ALZHEIMER'S patients ,TASK performance ,SEMANTICS (Philosophy) ,MATHEMATICAL analysis ,ALZHEIMER'S disease ,ASIANS ,CHI-squared test ,COGNITION disorders ,LANGUAGE & languages ,MATHEMATICS ,NEUROPSYCHOLOGICAL tests ,PROBLEM solving ,PSYCHOLOGICAL tests ,DISEASE complications - Abstract
Number processing disorder is an acquired deficit in mathematical skills commonly observed in Alzheimer’s disease (AD), usually as a consequence of neurological dysfunction. Common impairments include syntactic errors (800012 instead of 8012) and intrusion errors (8 thousand and 12 instead of eight thousand and twelve) in number transcoding tasks. This study aimed to understand the characterization of AD-related number processing disorder within an alphabetic language (English) and ideographical language (Chinese), and to investigate the differences between alphabetic and ideographic language processing. Chinese-speaking AD patients were hypothesized to make significantly more intrusion errors than English-speaking ones, due to the ideographical nature of both Chinese characters and Arabic numbers. A simplified number transcoding test derived from EC301 battery was administered to AD patients. Chinese-speaking AD patients made significantly more intrusion errors (p = 0.001) than English speakers. This demonstrates that number processing in an alphabetic language such as English does not function in the same manner as in Chinese. The impaired inhibition capability likely contributes to such observations due to its competitive lexical representation in brain for Chinese speakers. [ABSTRACT FROM PUBLISHER]
- Published
- 2016
- Full Text
- View/download PDF
35. Solutions of local fractional sine-Gordon equations
- Author
-
Doğan Demirhan, H. Karayer, Fevzi Büyükkiliç, and Ege Üniversitesi
- Subjects
Mathematical analysis ,[No Keywords] ,General Engineering ,General Physics and Astronomy ,010103 numerical & computational mathematics ,Conformable matrix ,01 natural sciences ,Domain (mathematical analysis) ,Fractional calculus ,010101 applied mathematics ,Nonlinear Sciences::Exactly Solvable and Integrable Systems ,Order (group theory) ,Sine ,0101 mathematics ,Nonlinear Sciences::Pattern Formation and Solitons ,Mathematics - Abstract
EgeUn###, In this paper, we study sine-Gordon equation in order to obtain exact solitary wave solutions in the domain of fractional calculus. By using the definition of conformable fractional derivative, we obtain analytical solutions of time, space and time-space fractional sine-Gordon equations. We analyze graphically the effect of fractional order on evolution of the kink and antikink type solitons.
- Published
- 2019
36. Beyond DIV, CURL and GRAD: modelling electromagnetic problems using algebraic topology
- Author
-
Krishnaswamy Sankaran
- Subjects
Curl (mathematics) ,Electromagnetics ,Equations ,05 social sciences ,Mathematical analysis ,Finite difference ,050301 education ,General Physics and Astronomy ,Differential Forms ,020206 networking & telecommunications ,02 engineering and technology ,Electromagnetic Modelling ,Finite element method ,Electronic, Optical and Magnetic Materials ,Algebraic Topology ,Computational Electromagnetics ,0202 electrical engineering, electronic engineering, information engineering ,Computational electromagnetics ,Applied mathematics ,Electrical and Electronic Engineering ,Differential algebraic geometry ,Spectral method ,0503 education ,Vector calculus ,Mathematics - Abstract
Have you ever questioned why do we almost always use vector calculus and differential equations in electromagnetics? Are these the only tools at our disposal for studying and modelling electromagnetic problems? Well, the answer is no and this paper is about an alternative approach to model electromagnetic problems using algebraic topology. This approach has a few advantages compared to the familiar differential formulation-based methods in modelling electromagnetic and multiphysics problems. In differential formulation we need one of the several numerical methods like finite difference, finite element, method of moments and spectral methods to obtain approximate solution to the electromagnetic problem. In contrast, algebraic topology-based method leads directly to discrete formulation using global quantities. Furthermore, in the case of electromagnetics, all underlying global quantities are scalars. Hence, there is no need for vector calculus. In addition, we also avoid interpolating local vector field quantities as required in several numerical methods. Though algebraic topology offers powerful and elegant tools for solving various engineering problems, many applied physicists and engineers are not familiar with this subject. This is partly due to the fact that most publications on this topic burden us with complicated mathematical analysis filled with convoluted jargons. If one can introduce the key ideas of algebraic topology using familiar concepts, computational and applied physics, and engineering community can appreciate and benefit from its advantages over methods based on differential formulation. With this goal, we present the main ideas of algebraic topology applied to electromagnetics problems.
- Published
- 2017
37. A meshless method and stability analysis for the nonlinear Schrodinger equation
- Author
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Yılmaz Dereli, Ayşe Gül Kaplan, and Anadolu Üniversitesi, Fen Fakültesi, Matematik Bölümü
- Subjects
Regularized meshless method ,Differential equation ,Gaussian ,Mathematical analysis ,General Engineering ,General Physics and Astronomy ,010103 numerical & computational mathematics ,01 natural sciences ,Stability (probability) ,010101 applied mathematics ,symbols.namesake ,Nonlinear Sciences::Exactly Solvable and Integrable Systems ,symbols ,0101 mathematics ,Nonlinear Sciences::Pattern Formation and Solitons ,Nonlinear Schrödinger equation ,Schrödinger's cat ,Mathematics - Abstract
WOS: 000407961100004, In this paper, the non-linear Schrodinger (NLS) equation was solved by a meshless method based on the moving least-squares approximation. Single-soliton solution and interaction of two colliding solitons were studied to validate the accuracy of the proposed method. In calculations, different weight functions in which Gaussian and Wendland's compactly supported functions were used. For the single-soliton solution of NLS equation whose analytical solution was known L-2, L-infinity error norms and invariants were calculated for two test problems. The obtained results were compared with both each other and some earlier results. Stability analysis of difference equation was done by applying the proposed method for NLS equation.
- Published
- 2017
38. On Inextensible flows of curves according to alternative moving frame
- Author
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Talat Körpinar
- Subjects
Quantitative Biology::Biomolecules ,Partial differential equation ,Euclidean space ,58E20 ,010102 general mathematics ,Mathematical analysis ,Frame (networking) ,Bonnet surface ,General Medicine ,31B30 ,01 natural sciences ,010101 applied mathematics ,(3) ,Fluid flow ,Moving frame ,Fluid dynamics ,Binormal images ,0101 mathematics ,Mathematics - Abstract
In this paper, we investigate inextensible flows of curves according to alternative moving frame in Euclidean space 𝔼3. Using the Prenet frame of the given curve, we present partial differential equations. The concepts with the inextensible flows are analyzed by using alternative moving frame.
- Published
- 2017
39. The Mittag–Leffler function and its application to the ultra-hyperbolic time-fractional diffusion-wave equation
- Author
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Gustavo Abel Dorrego
- Subjects
INTEGRALS TRANSFORMS ,Matemáticas ,FRACTIONAL DIFFERENTIAL EQUATION ,01 natural sciences ,Matemática Pura ,symbols.namesake ,Mittag-Leffler function ,Generalizations of the derivative ,0101 mathematics ,CAPUTO FRACTIONAL DERIVATIVE ,Computer Science::Distributed, Parallel, and Cluster Computing ,Mathematics ,Applied Mathematics ,Operator (physics) ,010102 general mathematics ,Mathematical analysis ,Wave equation ,ULTRA-HYPERBOLIC OPERATOR ,Fractional calculus ,010101 applied mathematics ,Fourier transform ,Quadratic form ,HILFER FRACTIONAL DERIVATIVE ,symbols ,MITTAG–LEFFLER-TYPE FUNCTION ,RIEMANNundefinedLIOUVILLE FRACTIONAL DERIVATIVE ,Laplace operator ,Analysis ,FOX'S H-FUNCTION ,CIENCIAS NATURALES Y EXACTAS - Abstract
In this paper we study an n-dimensional generalization of time-fractional diffusion-wave equation, where the Laplacian operator is replaced by the ultra-hyperbolic operator and the time-fractional derivative is taken in the Hilfer sense. The analytical solution is obtained in terms of the Fox's H-function, for which the inverse Fourier transform of a Mittag–Leffler-type function that contains in its argument a positive-definite quadratic form is calculated. Fil: Dorrego, Gustavo. Universidad Nacional del Nordeste. Facultad de Ciencias Exactas y Naturales y Agrimensura. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
- Published
- 2016
40. The boundedness of Hilbert transform in the local Morrey-Lorentz spaces
- Author
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A. Kucukaslan, Ayhan Serbetci, Canay Aykol, Vagif S. Guliyev, and Kırşehir Ahi Evran Üniversitesi, Fen-Edebiyat Fakültesi, Matematik Bölümü
- Subjects
Pure mathematics ,Applied Mathematics ,Operator (physics) ,Lorentz transformation ,010102 general mathematics ,Mathematical analysis ,Hardy operator ,modified Hilbert transform ,Space (mathematics) ,01 natural sciences ,Bounded mean oscillation ,Hilbert transform ,010101 applied mathematics ,symbols.namesake ,Local Morrey-Lorentz spaces ,Bounded function ,symbols ,Unitary operator ,0101 mathematics ,42B20 ,Analysis ,Mathematics ,42B35 ,47G10 - Abstract
WOS: 000371347600006 In this paper, we investigate the boundedness of the Hilbert transform H in the local Morrey-Lorentz spaces [GRAPHICS] , [GRAPHICS] , [GRAPHICS] . We prove that the operator H is bounded in [GRAPHICS] under the condition [GRAPHICS] , [GRAPHICS] . In the limiting case [GRAPHICS] , [GRAPHICS] , we prove that the operator H is bounded from the space [GRAPHICS] to the weak local Morrey-Lorentz space [GRAPHICS] . Also we show that for the limiting case [GRAPHICS] , [GRAPHICS] , the modified Hilbert transform [GRAPHICS] is bounded from the space [GRAPHICS] to the bounded mean oscillation space. Science Development Foundation under Republic of AzerbaijanScience Development Foundation (SDF) - Azerbaijan [EIF-2013-9(15)-46/10/1]; Presidium Azerbaijan National Academy of ScienceAzerbaijan National Academy of Sciences (ANAS) The research of V.S. Guliyev was partially supported by the grant of Science Development Foundation under the President of the Republic of Azerbaijan, Grant EIF-2013-9(15)-46/10/1 and by the grant of Presidium Azerbaijan National Academy of Science 2015.
- Published
- 2016
41. Inverse Sturm-Liouville problems with pseudospectral methods
- Author
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Christine Böckmann, Hasan Taşeli, H. Altundağ, and [Belirlenecek]
- Subjects
regular and singular inverse Sturm-Liouville problems ,Applied Mathematics ,65F18 ,Mathematical analysis ,pseudospectral method ,Institut für Mathematik ,Sturm–Liouville theory ,31A25 ,Regularization (mathematics) ,Computer Science Applications ,Singularity ,Gauss pseudospectral method ,Computational Theory and Mathematics ,Chebyshev pseudospectral method ,Pseudo-spectral method ,Pseudospectral optimal control ,Condition number ,regularization method ,Mathematics ,condition number - Abstract
In this paper a technique to obtain a first approximation for singular inverse Sturm-Liouville problems with a symmetrical potential is introduced. The singularity, as a result of unbounded domain (-infinity, infinity), is treated by considering numerically the asymptotic limit of the associated problem on a finite interval (-L, L). In spite of this treatment, the problem has still an ill-conditioned structure unlike the classical regular ones and needs regularization techniques. Direct computation of eigenvalues in iterative solution procedure is made by means of pseudospectral methods. A fairly detailed description of the numerical algorithm and its applications to specific examples are presented to illustrate the accuracy and convergence behaviour of the proposed approach. TUBITAK, the Scientific and Technical Research Council of TurkeyTurkiye Bilimsel ve Teknolojik Arastirma Kurumu (TUBITAK) This research was supported by a grant from TUBITAK, the Scientific and Technical Research Council of Turkey. WOS:000352953800005
- Published
- 2015
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