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We establish existence and uniqueness conditions for the solutions of difference equations with contracting compact operators in the metric space of two-sided sequences. [ABSTRACT FROM AUTHOR]

Given an integer k ≥ 2 and a real number ʇ ϵ[0,1], which graphs of edge density ʇ contain the largest number of k-edge stars? For k = 2 Ahlswede and Katona proved that asymptotically there cannot be more such stars than in a clique or in the complement of a clique (depending on the value of ʇ). Here we extend their result to all integers k ≥ 2. [ABSTRACT FROM AUTHOR]

The purpose of this research study is to understand how math majors conceptualize and make sense of pointwise convergence of sequence of functions in a series of in-depth qualitative interviews. Framed in APOS ( Dubinsky & McDonald, 2002 ) and VA (visual-analytic) strategy coordination ( Zazkis, Dubinsky & Dautermann, 1996 ) theoretical perspectives, the analysis showed that students demonstrated a diversity of mathematical behaviors associated mostly with the process level of understanding in APOS model. Yet a complete understanding of pointwise convergence at object level did not take place, students still also exhibited significant achievements in progression from process to object. The VA coordination also proved a beneficial mechanism in students’ making sense of pointwise convergence in a dynamic geometry environment. [ABSTRACT FROM AUTHOR]

In this paper, by using umbral calculus and umbral algebra methods, we derive several interesting identities and relations related to the modified and unification of the Bernoulli, Euler and Genocchi polynomials and numbers and the generalized (β-) Stirling numbers of the second kind. We also give some applications and remarks related to these numbers and polynomials. [ABSTRACT FROM AUTHOR]

In this paper we introduce the backward operator is ∇ and study the notion of ∇ -- Cauchy sequence using by almost (λmµn) convergence in χ² -- Riesz space and also some inclusion theorems are discussed. [ABSTRACT FROM AUTHOR]

A theorem of Kirby gives a necessary and sufficient condition for two framed links in [ABSTRACT FROM AUTHOR]

In this paper, we first investigate and present several sets of sufficient conditions for Carathéodory functions in the open unit disk U. We then apply the main results proven here in order to derive some conditions for starlike functions in U. Relevant connections with various known results are also considered. [ABSTRACT FROM AUTHOR]

We approximate fixed points of some iterative methods on a generalized Banach space setting. Earlier studies such as [5, 6, 7, 12] require that the operator involved is Fréchet-differentiable. In the present study we assume that the operator is only continuous. This way we extend the applicability of these methods to include generalized fractional calculus and problems from other areas. Some applications include generalized fractional calculus involving the Riemann-Liouville fractional integral and the Caputo fractional derivative. Fractional calculus is very important for its applications in many applied sciences. [ABSTRACT FROM AUTHOR]

Fatou's lemma is a classic fact in real analysis stating that the limit inferior of integrals of functions is greater than or equal to the integral of the inferior limit. This paper introduces a stronger inequality that holds uniformly for integrals on measurable subsets of a measurable space. The necessary and sufficient condition, under which this inequality holds for a sequence of finite measures converging in total variation, is provided. This statement is called the uniform Fatou lemma, and it holds under the minor assumption that all the integrals in the inequality are well-defined. The uniform Fatou lemma improves the classic Fatou lemma in the following directions: the uniform Fatou lemma states a more precise inequality, it provides the necessary and sufficient condition, and it deals with variable measures. Various corollaries of the uniform Fatou lemma are formulated. The examples in this paper demonstrate that: (a) the uniform Fatou lemma may indeed provide a more accurate inequality than the classic Fatou lemma; (b) the uniform Fatou lemma does not hold if convergence of measures in total variation is relaxed to setwise convergence. [ABSTRACT FROM AUTHOR]

In this article we discuss a variational aspect of a system of two equations arising in photometric stereo. Assuming that this system has two distinct solutions, we construct a minimizing sequence for any function lying on a segment joining these two solutions. In general, the system in question may have one, two, four or more than four solutions. [ABSTRACT FROM AUTHOR]

In this paper we have introduced the concept of geometric convergence of a sequence and determined the necessary and sufficient condition under which convergence follows from geometric convergence of a sequence in multiplicative sense. Corollaries allow this condition to be replaced by multiplicative analogues of Schmidt type slow oscillation condition or Landau type two-sided condition. [ABSTRACT FROM AUTHOR]

We develop integral calculus for quasi-standard smooth functions defined on the ring of Fermat reals. The approach is by proving the existence and uniqueness of primitives. Besides the classical integral formulas, we show the flexibility of the Cartesian closed framework of Fermat spaces to deal with infinite-dimensional integral operators. The total order relation between scalars permits to prove several classical order properties of these integrals and to study multiple integrals on Peano–Jordan-like integration domains. [ABSTRACT FROM AUTHOR]

In [1] and [6] Marx and Strohhäcker have proved that if f ∊ A is a convex function, then it has the property of starlikeness of order 1/2 . In [5, Theorem 9.5.6], P. T. Mocanu extended this result to the class A2 for a convex function of order - 1/2 . In this paper we extend the results proven by Marx and Strohhäcker and by P. T. Mocanu and we'll prove that, if the function f ∊ An, n ≥ 3, is a close-to-convex function, then it is starlike of order 1/2 . [ABSTRACT FROM AUTHOR]

In this paper, we introduce the following useful functional equations: f(x+y) + f(x-2y) + f(y-x)= f(x) f (∑i=1p xi/p-1) + p∑fi=2p ∑j=1,j≠ixj- pxi/p-1) + f(∑i=2pxi-x1/p-1) = f(x1)and prove the superstability and the Hyers-Ulam stability of (r; s; t)-J*-homomorphisms, associated with those, by using the fixed point method and the direct method. [ABSTRACT FROM AUTHOR]

In this paper, by considering Barnes-type Narumi polynomials of the second kind as well as poly-Cauchy polynomials of the second kind, we define and investigate the mixed-type polynomials of these polynomials. From the properties of Sheffer sequences of these polynomials arising from umbral calculus, we derive new and interesting identities. [ABSTRACT FROM AUTHOR]

Tangent fibrations generate a "multi-oored tower", while raising from one of its oors to the next one, one practically reiterates the previously performed actions. In this way, the "tower" admits a ladder-shaped structure. Raising to the first oors sufaces for iteratively performing the subsequent steps. The paper mainly studies the tangent functor. We describe the structure of multiple vector bundle which naturally appears on the oors, tangent maps, sector-forms, the lift of vector elds to upper oors. Further, we show how tangent groups of Lie groups lead to gauge theory, and explain in this context the meaning of covariant di erentiation. Finally, we will point out within the oors special subbundles - the osculating bundles, which play an essential role in classical theories. [ABSTRACT FROM AUTHOR]

This paper presents the results of a documentary investigation with the intention of substantiate how and why, and the level and depth of the topics used by the teacher in the classroom for the development of the mathematical knowledge on the part of higher level engineering students. The analysis of the mathematical object was made through the construction of conceptual cartography, being the core of the derivative concept. To construct the axes, the socio-formative theory of Sergio Tobón was used, together with the semiotic representation register of Raychmond Duval and Tall's mathematical advanced thought in the engineering context. The topic is a part of the Unit of learning: Differential and Integral Calculus. This corresponds to the first semester. The course lasts for a semester and is intended for students aged between 18 and 20 years. The research shows that by constructing a conceptual cartography involving at least 8 axes of analysis that the socioformation orientates, and taking mathematics in the context of careers offered by the educational institution, the teacher is allowed to place the thematic content in the appropriate level and depth, guiding in a possible treatment of knowledge to be brought into the classroom. [ABSTRACT FROM AUTHOR]

The article discusses the restriction of variables to integers in linear programming problems through the use of graphic linear system. It mentions the use of the corner point principle that states the presence of a unique optimal solution to a linear programming problem and the need for the problem to lie at a vertex. It cites the effective analysis of the corners with integer coordinates.

The article discusses the basics of a good mathematical problem. It mentions that a good mathematical problem should conform with the skills and attitudes of both the teachers and the students. It adds that the problem solver should decide on which technique he would use to solve the mathematical problem. It cites the benefits of using real life data on the part of the problem solver.

We obtain a vector-valued subordination principle for gα,gβ-regularized resolvent families which unified and improves various previous results in the literature. As a consequence, we establish new relations between solutions of different fractional Cauchy problems. To do that, we consider scaled Wright functions which are related to Mittag-Leffler functions, the fractional calculus, and stable Lévy processes. We study some interesting properties of these functions such as subordination (in the sense of Bochner), convolution properties, and their Laplace transforms. Finally we present some examples where we apply these results. [ABSTRACT FROM AUTHOR]

We prove that iterated Whitehead products of length ( n + 1) vanish in any value of an n-excisive functor in the sense of Goodwillie. We compare then different notions of homotopy nilpotency, from the Berstein-Ganea definition to the Biedermann-Dwyer one. The latter is strongly related to Goodwillie calculus and we analyze the vanishing of iterated Whitehead products in such objects. [ABSTRACT FROM AUTHOR]

This paper presents the dynamic response of Bernoulli-Euler homogeneous isotropic fractionally-damped simplysupported beam. The beam is appendaged to single-degree-of-freedom (SDOF) fractionally-damped N-oscillators and subjected to a moving load with a uniform velocity. The damping characteristics of the beam and oscillators are formally described in terms of fractional derivative of an arbitrary order. In the analysis, the initial conditions are assumed to be homogeneous, and the Laplace transform is combined with the used decomposition method to find the solution of the handled problem. Subsequently, curves are plotted to show the vibration of the utilized beam under different sets of parameters including different orders of fractional derivatives for both of the beam and oscillators. The numerical results obtained in this paper show that the dynamic response decreases as the number of absorbers attached to the beam increases, as both the damping-ratios of absorbers and beam increase the dynamic response decreases, and there are some critical values of fractional derivatives which are different from unity at which the beam has less dynamic response than that obtained for the full-order derivatives model. In addition, the obtained results show very good agreement with special case studies that were previously published in literature. [ABSTRACT FROM AUTHOR]

In this paper we investigate for which closed subsets P of the real line R there exists a continuous map from P onto P² and, if such a function exists, how smooth can it be. We show that there exists an infinitely many times differentiable function f:R → R² which maps an unbounded perfect set P onto P². At the same time, no continuously differentiable function f:R → R² can map a compact perfect set onto its square. Finally, we show that a disconnected compact perfect set P admits a continuous function from P onto P² if, and only if, P has uncountably many connected components. [ABSTRACT FROM AUTHOR]

The purpose of this article is to give a solution to a problem raised by A. Maliszewski in [5] by showing that any lower semicontinuous function can be represented as a sum of two lower semicontinuous strong Šwiątkowski functions. [ABSTRACT FROM AUTHOR]

It is presented a calculus method for balancing optimization of rod pumping units. The computer program having this mathematic model as base, it is flexible and allows any input parameter and provides the exact weight values of counterbalance for pumping units with direct schema. [ABSTRACT FROM AUTHOR]

Cauchy summation formula plays a central role in application of character calculus to many problems, from AGT-implied Nekrasov decomposition of conformal blocks to topological-vertex decompositions of link invariants. We briefly review the equivalence between Cauchy formula and expressibility of skew characters through the Littlewood-Richardson coefficients. As not-quite-a-trivial illustration we consider how this equivalence works in the case of plane partitions - at the simplest truly interesting level of just four boxes. [ABSTRACT FROM AUTHOR]

Using the AM-GM inequality, we solve the classic open-top box problem from first-semester calculus. [ABSTRACT FROM AUTHOR]