# Showing papers in "Publications De L'institut Mathematique in 2015"

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TL;DR: In this paper, the curvature properties of pseudosymmetry type of hypersurfaces in Euclidean spaces En+1, n ≥ 5, having three distinct nonzero principal curvatures λ 1, λ 2 and λ 3 of multiplicity 1, p and n-p-1, respectively, were determined.

Abstract: We determine curvature properties of pseudosymmetry type of hypersurfaces in
Euclidean spaces En+1, n ≥ 5, having three distinct nonzero principal
curvatures λ1, λ2 and λ3 of multiplicity 1, p and n-p-1, respectively For
some hypersurfaces having this property the sum of λ1, λ2 and λ3 is equal to
the trace of the shape operator of M We present an example of such
hypersurface

19 citations

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TL;DR: A survey of scaling arguments, both asymptotic and exact, in various areas of mathematical analysis and physics can be found in this paper, where the authors also discuss Fechner's law.

Abstract: We survey scaling arguments, both asymptotic (involving regular variation) and exact (involving self-similarity), in various areas of mathemat- ical analysis and mathematical physics. 1. Scaling and Fechner's law There is a sizeable body of theory to the effect that, where two related physically meaningful functions f and g have no natural scale in which to measure their units, and are reasonably smooth, then their relationship is given by a power law: (F)

13 citations

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TL;DR: In this paper, a new recurrence formula for sequences of divided differences was proposed, which simplifies the classical Newton-Girard identities relating power sums and elementary symmetric polynomials.

Abstract: We obtain a new recurrence formula for sequences of divided differences. In a
particular case, the recurrence formula simplifies the classical
Newton-Girard identities relating power sums and elementary symmetric
polynomials.

11 citations

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TL;DR: In this paper, the annihilating-ideal graph of R is defined as the graph AG(R) with the vertex set A(R)* = A(r)\{0} and two distinct vertices I====== and J are adjacent if and only if IJ = 0.

Abstract: Let R be a commutative ring with identity and A(R) be the set of ideals with
nonzero annihilator. The annihilating-ideal graph of R is defined as the
graph AG(R) with the vertex set A(R)* = A(R)\{0} and two distinct vertices I
and J are adjacent if and only if IJ = 0. In this paper, we study the
domination number of AG(R) and some connections between the domination
numbers of annihilating-ideal graphs and zero-divisor graphs are given.

10 citations

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9 citations

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TL;DR: In this paper, conformal and geodesic mappings of generalized equidistant spaces were studied and the existence of nontrivial mappings and invariant objects for these mappings were proved.

Abstract: We consider conformal and geodesic mappings of generalized equidistant
spaces. We prove the existence of mentioned nontrivial mappings and construct
examples of conformal and geodesic mapping of a 3-dimensional generalized
equidistant space. Also, we find some invariant objects (three tensors and
four which are not tensors) of special geodesic mapping of generalized
equidistant space. [Projekat Ministarstva nauke Republike Srbije, br. 174012]

8 citations

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TL;DR: A space X is almost Menger (weakly Menger) if for each sequence (Un : n N) of open covers of X there exists a sequence (Vn : n n, Vn is a finite subset of Un and ∪nN ∪{V : V Vn} = X as mentioned in this paper.

Abstract: A space X is almost Menger (weakly Menger) if for each sequence (Un : n N)
of open covers of X there exists a sequence (Vn : n N) such that for every
n N, Vn is a finite subset of Un and ∪nN ∪{V : V Vn} = X (respectively,
∪nN ∪{V : V Vn} = X). We investigate the relationships among almost
Menger spaces, weakly Menger spaces and Menger spaces, and also study
topological properties of almost Menger spaces and weakly Menger spaces.

8 citations

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TL;DR: In this article, a semisymmetric metric connection on a Riemannian manifold whose torsion tensor is almost pseudo symmetric was studied, and the associated 1-form of the connection on the almost pseudo-symmetric manifold was derived.

Abstract: We study a type of semisymmetric metric connection on a Riemannian manifold
whose torsion tensor is almost pseudo symmetric and the associated 1-form of
almost pseudo symmetric manifold is equal to the associated 1-form of the
semisymmetric metric connection.

6 citations

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TL;DR: In this paper, a class of regularization methods for solving least-squares problems with a convex constraint was studied and the convergence and convergence rate of these methods were proven for the power source imperfection condition.

Abstract: We study a class of regularization methods for solving least-squares
ill-posed problem with a convex constraint. Convergence and convergence rate
results are proven for the problems which satisfy so called power source
condition. All the results are obtained under the assumptions that, instead
of exact initial data, only their approximations are known.

5 citations

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TL;DR: In this article, it was shown that the Ricci soliton of an almost Kenmotsu manifold with conformal Reeb foliation is an Einstein metric and Ricci is expanding with λ = 4n.

Abstract: If the metric of an almost Kenmotsu manifold with conformal Reeb foliation is
a gradient Ricci soliton, then it is an Einstein metric and the Ricci
soliton is expanding. Moreover, let (M2n+1,Φ,ξ,η,g) be an almost
Kenmotsu manifold with ξ belonging to the (k,μ)′-nullity distribution and h
h≠0. If the metric g of M2n+1 is a gradient Ricci soliton, then M2n+1 is
locally isometric to the Riemannian product of an (n+1)-dimensional manifold
of constant sectional curvature -4 and a at n-dimensional manifold, also,
the Ricci soliton is expanding with λ = 4n.

5 citations

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TL;DR: In this article, the graph with the largest signless Laplacian spec- tral radius among all unicyclic graphs with fixed matching number was determined, and the largest eigenvalues of A(G and Q(G) are called the spectral radius and spectral radius of G, respectively.

Abstract: We determine the graph with the largest signless Laplacian spec- tral radius among all unicyclic graphs with fixed matching number. respectively. The largest eigenvalues of A(G) and Q(G) are called the spectral radius and the signless Laplacian spectral radius of G, denoted by �(G) and q(G), respectively. When G is connected, A(G) and Q(G) are nonegative irreducible matrix. By the Perron-Frobenius theory, �(G) is simple and has a unique positive unit eigenvector, so does q(G). We refer to such the eigenvector corresponding to q(G) as the Perron vector of G. Two distinct edges in a graph G are independent if they are not adjacent in G. A set of pairwise independent edges of G is called a matching in G. A matching of

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TL;DR: In this paper, the notion of λ-generalized contractions was investigated in uniform spaces endowed with a graph and discussed on the existence and uniqueness of fixed points for this type of contractions using the basic notion of entourages.

Abstract: We investigate the notion of λ-generalized contractions introduced by Ciric
in uniform spaces endowed with a graph and discuss on the existence and
uniqueness of fixed points for this type of contractions using the basic
entourages.

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TL;DR: In this article, a generalization of Segal's result for multisimplicial spaces is presented, providing an n-fold delooping of the classifying space of a category.

Abstract: Some sufficient conditions on a simplicial space X : Δop → Top guaranteeing
that X1 ≃ Ω|X| were given by Segal. We give a generalization of this result
for multisimplicial spaces. This generalization is appropriate for the
reduced bar construction, providing an n-fold delooping of the classifying
space of a category. [Projekat Ministarstva nauke Republike Srbije, br. ON174026]

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TL;DR: In this paper, it was shown that TVS-cone metric spaces are paracompact and that a homeomorphism f of a compact space is sufficiently expansive if and only if f is TVScone expansive.

Abstract: Metric spaces are cone metric spaces, and cone metric spaces are TVS-cone
metric spaces. We prove that TVS-cone metric spaces are paracompact. A
metrization theorem of TVS-cone metric spaces is obtained by a purely
topological tools. We obtain that a homeomorphism f of a compact space is
expansive if and only if f is TVS-cone expansive. In the end, for a TVS-cone
metric topology, a concrete metric generating the topology is constructed.

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TL;DR: In this paper, an infinite sequence of Chebyshev polynomials of the form: a0Tn(x) + a1Tn 1(x)) + · · · + amTn m(x), where (a0, a1,..., am) is a fixed m-tuple of real numbers, a0, am 6 0, Ti(x).

Abstract: We investigate an infinite sequence of polynomials of the form: a0Tn(x) + a1Tn 1(x) + · · · + amTn m(x) where (a0, a1, . . . , am) is a fixed m-tuple of real numbers, a0, am 6 0, Ti(x) are Chebyshev polynomials of the first kind, n = m, m + 1, m + 2, . . . Here we analyze the structure of the set of zeros of such polynomial, depending on A and its limit points when n tends to infinity. Also the expression of envelope of the polynomial is given. An application in number theory, more precise, in the theory of Pisot and Salem numbers, is presented.

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TL;DR: In this paper, the authors established a new upper bound on the sum of all coprime divisors of n. The main result is that Θ(n) 6 1.3007n log logn for all n > 570 571.

Abstract: We establish a new upper bound on the function � � (n), the sum of all coprime divisors of n. The main result is that � � (n) 6 1.3007n log logn for all n > 570 571.

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TL;DR: In this article, the Lagrangian corresponding to the Finsler and projective metrizability of sprays, particularly symmetric linear connections, is studied in terms of semi-basic 1-forms using the tools developed by Bucataru and Dahl.

Abstract: The metrizability of sprays, particularly symmetric linear connections, is
studied in terms of semi-basic 1-forms using the tools developed by Bucataru
and Dahl in [2]. We introduce a type of metrizability in relationship with
the Finsler and projective metrizability. The Lagrangian corresponding to the
Finsler metrizability as well as the Bucataru{Dahl characterization of
Finsler and projective metrizability are expressed by means of the Courant
structure on the big tangent bundle of TM. A byproduct of our computations is
that a at Riemannian metric, or generally an R-at Finslerian spray, yields
two complementary, but not orthogonally, Dirac structures on TbigTM. These
Dirac structures are also Lagrangian subbundles with respect to the natural
almost symplectic structure of TbigTM.

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TL;DR: In this article, the authors investigated if every quasi-minimal group is abelian and gave a positive answer for a pure group having a ∅-definable partial order with hundreds of uncountable chains.

Abstract: We investigate if every quasi-minimal group is abelian, and give a positive
answer for a quasi-minimal pure group having a ∅-definable partial order with
uncountable chains. We also relate two properties of a complete theory in a
countable language: the existence of a quasi-minimal model and the existence
of a strongly regular type. As a consequence we derive the equivalence of
conjectures on commutativity of quasi-minimal groups and commutativity of
regular groups.

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TL;DR: In this paper, the center of the ring of skew polynomials K[x;δ] was determined, where K is a field and δ is a non-zero derivation over K, and the term η(x) is the minimal polynomial of δ over K.

Abstract: We determine the center C(K[x;δ]) of the ring of skew polynomials K[x;δ],
where K is a field and δ is a non-zero derivation over K. We prove that
C(K[x;δ]) = ker δ, if δ is transcendental over K. On the contrary, if δ is
algebraic over K, then C(K[x;δ])=(ker δ)[η(x)]. The term η(x) is the minimal
polynomial of δ over K.

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TL;DR: In this article, the authors established the generalized superstability of differential equations of the nth-order with initial conditions and investigated the generalized inequalities of second-order differential equations with constant coefficients.

Abstract: We establish the generalized superstability of differential equations of
nth-order with initial conditions and investigate the generalized
superstability of differential equations of second order in the form of
y′′(x) + p(x)y′(x)+q(x)y(x) = 0 and the superstability of linear differential
equations with constant coefficients with initial conditions.

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TL;DR: Lower bounds for |M/N====== − α| in terms of N, where α = [0; f(1), f(2),...] are given in this paper.

Abstract: Let f(n) or the base-2 logarithm of f(n) be either d(n) (the divisor
function), σ(n) (the divisor-sum function), φ(n) (the Euler totient
function), ω(n) (the number of distinct prime factors of n) or Ω(n) (the
total number of prime factors of n). We present good lower bounds for |M/N
− α| in terms of N, where α = [0; f(1), f(2),...].

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TL;DR: In this article, Gevrey functions on the unit interval [-1, 1] were characterized as sums of holomorphic functions in specific neighborhoods of [-1; 1] and a simple proof for Dyn'kin's theorem of the existence of a pseudoanalytic extension for Gevreys on [1, 2] was presented.

Abstract: We characterize Gevrey functions on the unit interval [-1; 1] as sums of
holomorphic functions in specific neighborhoods of [-1; 1]. As an application
of our main theorem, we perform a simple proof for Dyn'kin's theorem of
pseudoanalytic extension for Gevrey classes on [-1; 1].

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TL;DR: In this article, the authors proposed generalizations of the mathematical model of magnetic insulation, described by multidimensional quasi potential ODE system or PDE system with a two-dimensional Laplace operator.

Abstract: We suggest generalizations of the mathematical model of magnetic insulation,
described by multidimensional quasi potential ODE system or PDE system with
two-dimensional Laplace operator. Existence conditions of the first integrals
of a certain type for the class of nonlinear quasi potential systems,
including the model vacuum diode are obtained. Integrability of the vacuum
diode models is justified. We find for PDE system the class of exact radially
symmetric solutions given by fractional-rational functions. The class of
systems with variable density, reduced to a similar system with the constant
current density by special transformations is specified. The class of exact
solutions of the non-singular boundary-value problem in annular domain is
found.

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TL;DR: In this paper, the generalized local cohomology modules were studied with respect to an arbitrary ideal I of R, and it was shown that the Bass number of the generalized LLC modules is bounded above by Σtj=0μr(p, t−jExtR (M,HjI (N)) for all nonnegative integers r, t and all p Spec(R).

Abstract: Let R be a Noetherian ring, M a finitely generated R-module and N an
arbitrary R-module. We consider the generalized local cohomology modules,
with respect to an arbitrary ideal I of R, and prove that, for all
nonnegative integers r, t and all p Spec(R) the Bass number μr(p,HtI
(M,N)) is bounded above by Σtj=0μr(p, t−jExtR (M,HjI (N))). A corollary
is that Ass (HtI (M,N) Utj=0 Ass (t−jExtR (M,HjI(N))). In a
slightly different direction, we also present some well known results about
generalized local cohomology modules.

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TL;DR: In this paper, the authors define and investigate the class of almost ω 1 n-simply presented p-torsion groups, which class properly contains the subclasses of almost ✓ 1 − 1 n − presented groups.

Abstract: We define and investigate the class of almost ω1-n-simply presented p-torsion
abelian groups, which class properly contains the subclasses of almost
n-simply presented groups and ω1-n-simply presented groups, respectively.
The obtained results generalize those obtained by us in Korean J. Math.
(2014) and J. Algebra Appl. (2015).

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TL;DR: In this article, the wave front and the Sobolev wave front of a distribution f 2 D'(R d ) in terms of Fourier series coefficients were described in the product of periodic distributions.

Abstract: Motivated by the product of periodic distributions, we give a new description of the wave front and the Sobolev-type wave front of a distribution f 2 D ' (R d ) in terms of Fourier series coefficients.

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TL;DR: In this article, the authors apply the theory of Grobner bases to the study of signed, symmetric polyomino tilings of planar domains, and show that the triangular regions TN = T3k−1 and TN =T3k in a====== hexagonal lattice admit a signed tiling by three-in-line polyminoes (tribones) symmetric with respect to the 120◦ rotation of the triangle if and======

Abstract: We apply the theory of Grobner bases to the study of signed, symmetric
polyomino tilings of planar domains. Complementing the results of Conway and
Lagarias we show that the triangular regions TN = T3k−1 and TN = T3k in a
hexagonal lattice admit a signed tiling by three-in-line polyominoes
(tribones) symmetric with respect to the 120◦ rotation of the triangle if and
only if either N = 27r − 1 or N = 27r for some integer r > 0. The method
applied is quite general and can be adapted to a large class of symmetric
tiling problems. [Projekat Ministarstva nauke Republike Srbije br. 174020 i
br. 174034]

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TL;DR: In this paper, Hopf algebras over projection functions of the complex vector CX are studied for computing inversion formulas from discrete mathematics using a Hopf calculus of projection functions introduced in this way.

Abstract: We study Hopf algebras over projection functions of the complex vector CX
appropriate for computing inversion formulas from discrete mathematics Using
calculus of projection functions introduced in this way, we derived various
inversion formulas, including Gould’s inversion formula and its
generalizations [Projekat Ministarstva nauke Republike Srbije, br III
44006]

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TL;DR: Kim et al. as discussed by the authors showed that for arbitrary x √ n ≥ 0, {xn}n≥0 converges strongly to p F(T) such that F(t) = {pK:Tp=p}.

Abstract: Let K be a nonempty closed convex subset of a real Banach space X,T:K → K
a nearly uniformly L-Lipschitzian (with sequence {rn}) asymptotically
generalized Φ-hemicontractive mapping (with sequence kn [1,∞), lim n→∞ kn =
1) such that F(T) = {pK:Tp=p}. Let {αn}n≥0, {βkn}n≥0 be real
sequences in [0,1] satisfying the conditions: (i) Σn≥0 αn = 1 (ii) limn→∞
αn, βkn = 0, k = 1, 2,..., p−1. For arbitrary x0 K, let {xn}n≥0 be a
multi-step sequence iteratively defined by xn+1=(1−αn)xn + αnTny1n, n≥0, ykn = (1 − βkn )xn + βkn Tnyk+1n, k = 1,2,..., p−2 (0.1), yp−1n=(1− βp−1n)xn + βp−1n Tnxn, n ≥ 0, p ≥ 2. Then, {xn}n≥0 converges strongly to p F(T). The result proved in this note significantly improve the results of Kim et al. [2].