Search

The purpose of the paper is to study the uniqueness of meromorphic functions sharing a nonzero polynomial. The results of the paper improve and generalize the recent results due to X. B. Zhang and J. F. Xu [19]. We also solve an open problem as posed in the last section of [19].

I present a construction of connected affine algebraic supergroups G_V associated with simple Lie superalgebras g of Cartan type and with g-modules V. Conversely, I prove that every connected affine algebraic supergroup whose tangent Lie superalgebra is of Cartan type is necessarily isomorphic to one of the supergroups G_V that I introduced. In particular, the supergroup constructed in this way associated with g := W(n) and its standard representation is described somewhat more in detail. In addition, *** an "Erratum" is added here *** after the main text to fix a mistake which was kindly pointed out to the author by prof. Masuoka after the paper was published: this "Erratum" is accepted for publication in "Forum Mathematicum", it appears here in its final form (but prior to proofreading). In it, I also explain more in detail the *Existence Theorem* for algebraic supergroups of Cartan type which comes out of the main result in the original paper., Comment: Main file: La-TeX file, 47 pages, already published (see below). Erratum: La-TeX file, 6 pages, to appear (see below). For the main file, the original publication is available at www.degruyter.com (cf. the journal reference here below)

A structure on terms of faster convergent series is studied in the paper. Necessary and sufficient conditions for the existence of faster convergent series with different types of terms are found. A faster convergence criteria for certain Kummer’s series is proved in this paper.

In this paper, we study Clifford–Wolf translations of Finsler spaces. We give a characterization of those Clifford–Wolf translations generated by Killing vector fields. In particular, we show that there is a natural interrelation between the local one-parameter groups of Clifford–Wolf translations and the Killing vector fields of constant length. In the special case of homogeneous Randers spaces, we give some explicit sufficient and necessary conditions for a Killing vector field to have a constant length, in which case the local one-parameter group of isometries generated by the Killing field consist of Clifford–Wolf translations. Finally, we construct explicit examples to explain some of the results of this paper.

In this paper, we give some sufficient conditions for f : X → H to be a diffeomorphism, where X is a Banach space and H is a Hilbert space. The proof of the result is based on the mountain pass theorem. Using this result, in the final part of the paper, we prove an existence theorem for some class of integro-differential equations.

The aim of this paper is to study the representation theory of quantum Schubert cells. Let 𝔤 $\mathfrak {g}$ be a simple complex Lie algebra. To each element w of the Weyl group W of 𝔤 $\mathfrak {g}$ , De Concini, Kac and Procesi have attached a subalgebra U q [ w ] $U_q[w]$ of the quantised enveloping algebra U q ( 𝔤 ) $U_q(\mathfrak {g})$ . Recently, Yakimov showed that these algebras can be interpreted as the (quantum) Schubert cells on quantum flag manifolds. In this paper, we study the primitive ideals of U q [ w ] $U_q[w]$ . More precisely, it follows from the Stratification Theorem of Goodearl and Letzter, and from recent works of Mériaux–Cauchon and Yakimov, that the primitive spectrum of U q [ w ] $U_q[w]$ admits a stratification indexed by those elements v ∈ W $v \in W$ with v ≤ w $v \le w$ in the Bruhat order. Moreover each stratum is homeomorphic to the spectrum of maximal ideals of a torus. The main result of this paper gives an explicit formula for the dimension of the stratum associated to a pair v ≤ w $v \le w$ .

A class of (right) Rickart rings, called strong, is isolated. In particular, every Rickart *-ring is strong. It is shown in the paper that every strong Rickart ring R admits a binary operation which turns R into a right normal band having an upper bound property with respect to its natural order ≤; such bands are known as right normal skew nearlattices. The poset (R, ≤) is relatively orthocomplemented; in particular, every initial segment in it is orthomodular.The order ≤ is actually a version of the so called right-star order. The one-sided star orders are well-investigated for matrices and recently have been generalized to bounded linear Hilbert space operators and to abstract Rickart *-rings. The paper demonstrates that they can successfully be treated also in Rickart rings without involution.

Let SH be the class of functions f = h+g that are harmonic univalent and sense-preserving in the open unit disk U = { z : |z| < 1} for which f (0) = f'(0)-1=0. In this paper, we introduce and study a subclass H( α, β) of the class SH and the subclass NH( α, β) with negative coefficients. We obtain basic results involving sufficient coefficient conditions for a function in the subclass H( α, β) and we show that these conditions are also necessary for negative coefficients, distortion bounds, extreme points, convolution and convex combinations. In this paper an attempt has also been made to discuss some results that uncover some of the connections of hypergeometric functions with a subclass of harmonic univalent functions.

A Hom-structure on a Lie algebra (g,[,]) is a linear map σ W g σ g which satisfies the Hom-Jacobi identity: [σ(x), [y,z]] + [σ(y), [z,x]] + [σ(z),[x,y]] = 0 for all x; y; z ∈ g. A Hom-structure is referred to as multiplicative if it is also a Lie algebra homomorphism. This paper aims to determine explicitly all the Homstructures on the finite-dimensional semi-simple Lie algebras over an algebraically closed field of characteristic zero. As a Hom-structure on a Lie algebra is not necessarily a Lie algebra homomorphism, the method developed for multiplicative Hom-structures by Jin and Li in [J. Algebra 319 (2008): 1398–1408] does not work again in our case. The critical technique used in this paper, which is completely different from that in [J. Algebra 319 (2008): 1398– 1408], is that we characterize the Hom-structures on a semi-simple Lie algebra g by introducing certain reduction methods and using the software GAP. The results not only improve the earlier ones in [J. Algebra 319 (2008): 1398– 1408], but also correct an error in the conclusion for the 3-dimensional simple Lie algebra sl2. In particular, we find an interesting fact that all the Hom-structures on sl2 constitute a 6-dimensional Jordan algebra in the usual way.

In this paper we construct explicitly a square integrable residual automorphic representation of the special orthogonal group $SO_{2n}$, through Eisenstein series. We show that this representation comes from an elliptic Arthur parameter $\psi$ and appears in the space $L^2(SO_{2n}(\mathbb{Q})\backslash SO_{2n}(\mathbb{A}_{\mathbb{Q}}))$ with multiplicity one. Next, we consider parameters whose Hecke matrices, at the unramified places, have eigenvalues bigger (in absolute value), than those of the parameter constructed before. The main result is, that these parameters cannot be cuspidal. We establish bounds for the eigenvalues of Hecke operators, as consequences of Arthur's conjectures for $SO_{2n}$. Next, we calculate the character and the twisted characters for the representations that we constructed. Finally, we find the composition of the global and local Arthur's packets associated to our parameter $\psi$. All the results in this paper are true if we replace $\mathbb{Q}$ by any number field $F$., Comment: 39 pages

The paper starts from the suggestion of R. E. Kalman that additional information on nonlinearity slope may improve the sufficient conditions for absolute stability. This leads to the so called systems with augmented dynamics. Motivated also by the problem of the PIO II aircraft oscillations-self sustained oscillations induced by the saturation nonlinearities, which are both sector and slope restricted-the paper considers a generalization of the Yakubovich criterion to the case of the systems with critical and unstable linear part. The same generalization concerns a quite well known stability criterion where only slope restrictions are taken into account: the published version is improved by using all advantages of the Liapunov method and of the frequency domain stability inequalities. The results are illustrated by several applications.

There are two definitions of Γ-semigroups and investigations for both of them in the bibliography. The definition given by Sen in 1981, and the definition given by Sen and Saha in 1986. In this paper we show the way we pass from ordered semigroups to ordered Γ-semigroups no matter which one of the two definitions we use. Moreover we show that, exactly as in ordered semigroups, in many results of ordered Γ-semigroups points do not play any essential role, but the sets, which shows their pointless character. Under the methodology using in this paper, all the results of ordered semigroups can be transferred into ordered Γ-semigroups.

While a large amount of papers are dealing with robust multilevel methods and algorithms for linear FEM elliptic systems, the related higher order FEM problems are much less studied. Moreover, we know that the standard hierarchical basis two-level splittings deteriorate for strongly anisotropic problems. A first robust multilevel preconditioner for higher order FEM systems obtained after discretizations of elliptic problems with an anisotropic diffusion tensor is presented in this paper. We study the behavior of the constant in the strengthened CBS inequality for semi-coarsening mesh refinement which is a quality measure for hierarchical two-level splittings of the considered biquadratic FEM stiffness matrices. The presented new theoretical estimates are confirmed by numerically computed CBS constants for a rich set of parameters (coarsening factor and anisotropy ratio). In the paper we consider also the problem of solving efficiently systems with the pivot block matrices arising in the hierarchical basis two-level splittings. Combining the proven uniform estimates with the theory of the Algebraic MultiLevel Iteration (AMLI) methods we obtain an optimal order multilevel algorithm whose total computational cost is proportional to the size of the discrete problem with a proportionality constant independent of the anisotropy ratio.

The present paper continues the series of the papers [Amaglobeli and Bokelavadze, Exponential groups. III. Groups which are exact for tensor complement, Herald of Omsk University, 2009, Myasnikov and Remeslennikov, Sibirsk. Mat. Zh. 35: 1106–1118, 1994, Myasnikov and Remeslennikov, Internat. J. Algebra Comput. 6: 687–711, 1996] and is dedicated to the construction of basic principles of the theory of power group varieties and tensor completions of groups in a variety. We study the relationship between free groups of a given variety for various rings of scalars. Varieties of abelian power groups are described.

We compute the integral cohomology ring of configuration spaces of two points on a given real projective space. Apart from an integral class, the resulting ring is a quotient of the known integral cohomology of the dihedral group of order 8 (in the case of unordered configurations, thus has only 2- and 4-torsion) or of the elementary abelian 2-group of rank 2 (in the case of ordered configurations, thus has only 2-torsion). As an application, we complete the computation of the symmetric topological complexity of real projective spaces of dimensions of the form 2^i+j for non-negative i and j with j, The results in this paper include those in arXiv:1004.0746, but the methods are different; here we depend on Bockstein spectral sequence calculations. While arXiv:1004.0746 deals only with additive structures, we now obtain full descriptions of the relevant cohomology rings. Further, this paper is more condensed than arXiv:1004.0746, from 41 pages in the latter, to the current 28 pages

This paper is a preliminary work on Heisenberg group domains, devoted to the study of the Green’s function for the Kohn Laplacian on domains far away from the set of characteristic points. We give some estimates of the Green’s function, its regular part and their derivatives analogous to those proved by A. Bahri, Y.Y. Li, O. Rey in [1], and O. Rey in [16] for Euclidean domains. While the study of such functions on the set of characteristic points of the given domain will be discussed in a forthcoming paper.

This paper is devoted to the numerical solution of nonlinear elliptic partial differential equations. Such problems describe various phenomena in science. An approach that exploits Hilbert space theory in the numerical study of elliptic PDEs is the idea of preconditioning operators. In this survey paper we briefly summarize the main lines of this theory with various applications.

In this paper we prove some general theorems on the existence of continuous order-preserving functions on topological spaces with a continuous preorder. We use the concepts of network and netweight to prove new continuous representation theorems and we establish our main results for topological spaces that are countable unions of subspaces. Some results in the literature on path-connected, locally connected and separably connected spaces are shown to be consequences of the general theorems proved in the paper. Finally, we prove a continuous representation theorem for hereditarily separable spaces.

Dear Reader, please find the third and last part of a series of papers on the singular perturbation of the first eigenfunction associated to a non self-adjoint second order elliptic operators. This series started in 1999 and we presented the early results in 2000 at Columbia University. We published two notes in CRAS in 2001 and 2005 summarizing our results. The present paper contains the proofs of the announced theorems and many open questions. We tried to publish these results in the the top tier of mathematical journals (Annals, Acta, Duke...) but our results were not deemed sufficiently interesting for them and probably not trendy enough. Some of you may like this work, so here it is. Best Regards, Ivan and David. We study the semi-classical limits of the first eigenfunction of a positive second order operator on a compact Riemannian manifold, when the diffusion constant $\epsilon$ goes to zero. If the drift of the diffusion is given by a Morse-Smale vector field $b$, the limits of the eigenfunctions concentrate on the recurrent set of $b$. A blow-up analysis enables us to find the main properties of the limit measures on a recurrent set., Comment: around 70 pages. Can't be read in one shot

In this paper we analyze the Chosen Target Forced Prefix (CTFP) preimage resistance security notion for hash functions firstly introduced in [Kelsey, J.-Kohno, T.: Herding hash functions and the Nostradamus attack, in: Advances in Cryptology-EUROCRYPT ’06, 25th Annual Internat. Conf. on the Theory and Appl. of Cryptographic Techniques (S. Vaudenay, ed.), St. Peters- burg, Russia, 2006, Lecture Notes in Comput. Sci., Vol. 4004, Springer-Verlag, Berlin, 2006, pp. 183-200]. We give a formal definition of this property in hash function family settings and work out all the implications and separations be- tween the CTFP preimage resistance and other standard notions of hash function security (preimage resistance, collision resistance, etc.). This paper follows the work of [Rogaway, P.-Shrimpton, T.: Cryptographic hash-function basics: Def- initions, implications, and separations for preimage resistance, second-preimage resistance, and collision resistance, in: Fast Software Encryption, 11th Interna- tional Workshop-FSE ’04 (B. Roy et al., eds.), Delhi, India, 2004, Lecture Notes in Comput. Sci., Vol. 3017, Springer-Verlag, Berlin, 2004, pp. 371-388], where they define seven basic notions of hash function security and examine all the relationships among these notions. We also define a new property for security of hash function families-always CTFP preimage resistance, which guarantees CTFP security for all the hash functions in the family.

This paper deals with cryptanalysis of one hash function based on isotopy of quasigroups [J. Dvorský, E. Ochodková, V. Snášel: Hash functionbased on quasigroups, in: Proc. of Mikulàšska kryptobesídka, Praha, 2001, pp. 27-36. (In Czech)], [J. Dvorský, E. Ochodková, V. Snášel: Hash functionsbased on large quasigroups, in: Proc. of Velikonoční kryptologie, Brno, 2002, pp. 1-8. (In Czech)]. Our work enhances the paper [M. Vojvoda: Cryptanalysisof one hash function based on quasigroup, Tatra Mt. Math. Publ. 29 (2004), 173-181], where the simplified studied hash function, based only on the quasigroup of modular subtraction, was successfully cryptanalysed. In this paper we show how to construct collisions, 2nd preimages, and also preimages for the full hash function based on isotopy of quasigroups.

This paper deals with the steganographic algorithm LSB (modification of the Least Significant Bits) in JPEG images. The focus is on minimizing of the number of modified DCT coefficients using (2k − 1, 2k − k − 1) Hamming codes. Experimental part of the paper examines the dependencies between the coding, efficiency and saturation.

In two earlier papers [GAVRILUŢ, A.: A Gould type integral with respect to a multisubmeasure, Math. Slovaca 58 (2008), 1–20] and [Gavriluţ, A.: On some properties of the Gould type integral with respect to a multisubmeasure, An. Ştiinţ. Univ. Al. I. Cuza Iaşi. Mat. (N.S.) 52 (2006), 177–194], we defined and studied a Gould type integral for a real valued, bounded function with respect to a multisubmeasure having finite variation. In this paper, we introduce and study the properties of a Gould type integral in the general setting: the function may be unbounded and the variation of the multisubmeasure may be infinite.

Many algebras arising in logic have a lattice structure with intervals being equipped with antitone involutions. It has been proved in [CHK1] that these lattices are in a one-to-one correspondence with so-called basic algebras. In the recent papers [BOTUR, M.—HALAŠ, R.: Finite commutative basic algebras are MV-algebras, J. Mult.-Valued Logic Soft Comput. (To appear)]. and [BOTUR, M.—HALAŠ, R.: Complete commutative basic algebras, Order 24 (2007), 89–105] we have proved that every finite commutative basic algebra is an MV-algebra, and that every complete commutative basic algebra is a subdirect product of chains. The paper solves in negative the open question posed in [BOTUR, M.—HALAŠ, R.: Complete commutative basic algebras, Order 24 (2007), 89–105] whether every commutative basic algebra on the interval [0, 1] of the reals has to be an MV-algebra.

In this paper we define the notion of relative subalgebra of an MV-algebra A. A particular case of this notion is the notion of interval subalgebra of A; this has been already studied in the literature. Applying these notions, two new categories denoted as r and int are introduced. In both cases the objects are MV-algebras, but the homomorphisms are defined by means of relative subalgebras or by interval subalgebras, respectively. The relations occurring between these categories and the category of all MV-algebras with usual homomorphisms are investigated. The main results of the paper deal with one-generated free MV-algebras in the variety generated by the finite chains S i, i ⩽ p (p varying over the set of all positive integers) and their relations to certain relative subalgebras of the cyclic free MV-algebra.

One-dimensional propagation phenomena of physics and technology are described by boundary value problems for hyperbolic partial differential equations in one space dimension. Since the paper of J. Bernoulli published in 1728, functional equations are usually associated with such problems, the best known in the last decades being the neutral differential equations with deviated arguments. The distortionless propagation corresponds to the case of the equations with pointwise (lumped) time delays. The present paper will consider some applications of these equations in nuclear and power engineering, engineering mechanics, hydraulics. The basic model validation steps (basic theory, invariant sets, inherent stability) are discussed.

We consider the problem of making statistical inference about the mean of a normal distribution based on a random sample of quantized (digitized) observations. This problem arises, for example, in a measurement process with errors drawn from a normal distribution and with a measurement device or process with a known resolution, such as the resolution of an analog-to-digital converter or another digital instrument. In this paper we investigate the effect of quantization on subsequent statistical inference about the true mean. If the standard deviation of the measurement error is large with respect to the resolution of the indicating measurement device, the effect of quantization (digitization) diminishes and standard statistical inference is still valid. Hence, in this paper we consider situations where the standard deviation of the measurement error is relatively small. By Monte Carlo simulations we compare small sample properties of the interval estimators of the mean based on standard approach (i.e. by ignoring the fact that the measurements have been quantized) with some recently suggested methods, including the interval estimators based on maximum likelihood approach and the fiducial approach. The paper extends the original study by Hannig et al. (2007).

In this paper, sufficient conditions are obtained, so that the second order neutral delay differential equation $$ (r(t)(y(t) - p(t)y(t - \tau ))')' + q(t)G(y(h(t)) = f(t) $$ has a positive and bounded solution, where q, h, f ∈ C ([0, ∞), ℝ) such that q(t) ≥ 0, but ≢ 0, h(t) ≤ t, h(t) → ∞ as t → ∞, r ∈ C (1) ([0, ∞), (0, ∞)), p ∈ C (2) [0, ∞), ℝ), G ∈ C(ℝ, ℝ) and τ ∈ ℝ+. In our work r(t) ≡ 1 is admissible and neither we assume G is non-decreasing, xG(x) > 0 for x ≠ 0, nor we take G is Lipschitzian. Hence the results of this paper improve many recent results.

In a paper of Thuswaldner and Tichy, a version of Waring’s problem with restrictions on the sum of digits was considered. This paper is devoted to a generalization of their result to arbitrary completely q-additive functions.

In this paper we study 2D Fornasini–Marchesini and 2D Givone–Roesser models from the viewpoint developed in our recent paper [Lomadze, Rogers, Wood, Georgian Math. J. 15: 139–157, 2008]. We give necessary and sufficient conditions for a behavior to be expressable in Fornasini–Marchesini or Givone–Roesser form, and a canonical realization when the conditions are met. We also study the regularity, controllability and autonomy of these models. In particular, we provide the concepts of controllability in the sense of Kalman for each model, and show that they agree with the behavioral controllability as defined in [Lomadze, Rogers, Wood, Georgian Math. J. 15: 139–157, 2008].

Suppose G is an abelian group with a p-subgroup H and R is a commutative unitary ring of prime characteristic p with trivial nil-radical. We give a complete description up to isomorphism of the maximal divisi- ble subgroups of 1 + I(RG;H) and (1 + I(RG;H))=H, respectively, where I(RG;H) denotes the relative augmentation ideal of the group algebra RG with respect to H. This paper terminates a series of works by the author on the topic, flrst of which are (4) and (5). I. Introduction Throughout the present paper, we assume that G is an abelian group with p- component of torsion elements Gp and p-socle G(p) and that R is a commutative ring with identity (often called a commutative unitary ring) of prime charac- teristic p with the ideal of nilpotent elements N(R) and with maximal perfect (often termed maximal divisible) subring dR. For such R and G, where G is written multiplicatively as it is customary when dealing with group rings, RG denotes the group algebra of G over R with the normalized group V (RG) of invertible elements in RG (often named as normalized units) and its subgroup of p-torsion elements S(RG). For a subgroup H of G, I(RG;H) denotes the relative augmentation ideal of RG with respect to H. When HGp, we denote by S(RG;H) the sum 1+I(RG;H); clearly, S(RG;H) is a subgroup of S(RG) and S(RG) = S(RG;G) when G = Gp. All other notions as well as the notation are standard and follow essentially those from the existing literature with the exception of dG which means the maximal divisible subgroup of G and G ⁄ the maximal p-divisible subgroup of G. The isomorphism classiflcation of the maximal divisible subgroup dS(RG) of S(RG) was started by Mollov{Nachev in (13) when G is a p-group, and independently by Mollov in (9) when R is a fleld. Later, Nachev generalized in (10) and (11) these results to arbitrary abelian groups and arbitrary commutative unitary rings of prime characteristic. Concerning the mixed and torsion cases, we classify in (4) and (6) dV (RG) up to isomorphism assuming that either G is p-mixed and R is a fleld, or G is a special torsion group and R is a special decomposable or indecomposable

This paper addresses questions related to the existence and construction of large sets of t-(v, k, λ) designs. It contains material from my talk in the Combinatorial Designs Conference in honor of Alex Rosa’s 70th birthday, which took place in beautiful Bratislava, in July, 2007. Naturally, only a small number of “highlight” topics could be included, and for the most part these involve the use of symmetry, that is, it is assumed that the particular designs or large sets of designs, are invariant under a prescribed group of automorphisms. I present almost no proofs, but give references so that the reader can find a much wider repertory of theorems and constructions in the literature. For completeness, I include the statement of a few recursive constructions. The latter are extremely important on their own right, and deserve extensive attention elsewhere. I hope the reader becomes interested in the intriguing open problems posed at the end of the paper and succeeds in solving some of them.

For each positive integer k, we investigate the L-function attached to the k-th symmetric power of the F-crystal associated to the family of cubic exponential sums of x 3 + ‚x where ‚ runs over Fp. We explore its rationality, fleld of deflnition, degree, trivial factors, functional equation, and Newton polygon. The paper is essentially self-contained, due to the remarkable and attractive nature of Dwork’s p-adic theory. A novel feature of this paper is an extension of Dwork’s efiective decomposition theory when k < p. This allows for explicit computations in the associated p-adic cohomology. In particular, the action of Frobenius on the (primitive) cohomology spaces may be explicitly studied.

The present paper is devoted to the investigation of one dyna- mical three-dimensional mathematical model of the ∞uid-solid interaction. The variational formulation of the corresponding initial boundary problem is considered and a problem for abstract second order evolution equation is for- mulated, which is a generalization of the three-dimensional initial boundary value problem. For the stated abstract problem the existence and uniqueness of solution, and the energy equality are proved, which yield the corresponding result for the dynamical three-dimensional problem of ∞uid-solid interaction. Mathematical models of the interaction of ∞uid and solid, gas and solid are widely used when investigating various physical, ecological and geophysical pro- cesses. In particular, mathematical models of the interaction of a solid and a ∞uid or a gas are employed to study the motion of aircraft or submarines; mathematical modeling of interaction of ∞uid and a solid is important for the investigation of sea shore protection problems. Mathematical models of the in- teraction of media with difierent physical properties, the corresponding initial boundary value problems and the numerical methods of solution are studied in (1{4). The present paper deals with the dynamical three-dimensional mathemati- cal model of the interaction of an elastic solid and a viscous barotropic ∞uid considered in (1, 2), where the initial boundary value problems with homoge- neous Dirichlet boundary conditions and homogeneous initial conditions were studied applying Laplace transform and the theory of semigroups. We consider an initial-boundary value problem with mixed Dirichlet and Neumann bound- ary conditions and nonhomogeneous initial conditions. In order to investigate a three-dimensional problem we formulate the variational problem for an abstract second order evolution equation which is a generalization of the second order evolution equation studied in (5, 6). We investigate the existence and unique- ness of a solution and prove the energy equality which makes it possible to obtain the continuous dependence of the solution on the given vector functions in suitable spaces. As a consequence, we obtain the well posedness theorem for the dynamical three-dimensional ∞uid-solid interaction problem. For each real s ‚ 0; we denote by H s (›) and H s ( • i) the Sobolev spaces of order s based on H 0 (›) = L 2 (›) and H 0 ( • i) = L 2 ( • i), respectively, where

This paper considers an established model of a parabolic-hyperbolic coupled system of two PDEs, which arises when an elastic structure is immersed in a fluid. Coupling occurs at the interface between the two media. Semigroup well-posedness on the space of finite energy for {𝑤, 𝑤𝑡, 𝑢} was established in [Contemp. Math. 440: 15–54, 2007]. Here, [𝑤, 𝑤𝑡] are the displacement and the velocity of the structure, while 𝑢 is the velocity of the fluid. The domain D(A) of the generator A does not carry any smoothing in the 𝑤-variable (its resolvent 𝑅(λ, A) is not compact on this component space). This raises the issue of higher regularity of solutions. This paper then shows that the mechanical displacement, fluid velocity, and pressure terms do enjoy a greater regularity if, in addition to the I.C. {𝑤0, 𝑤1, 𝑢0} ∈ D(A), one also has 𝑤0 in (𝐻2(Ω𝑠))𝑑.

In a previous author’s paper, sequential convergences on an MV-algebra Open image in new window have been studied; the Urysohn’s axiom was assumed to be valid. The system of all such convergences was denoted by Conv Open image in new window . In the present paper we investigate analogous questions without supposing the validity of the Urysohn’s axiom; the corresponding system of convergences is denoted by conv Open image in new window . Both Conv Open image in new window and conv Open image in new window are partially ordered by the set-theoretical inclusion. We deal with the properties of conv 289-6 and the relations between conv Open image in new window and Conv Open image in new window . We prove that each interval of conv Open image in new window is a distributive lattice. The system conv Open image in new window has the least element, but it does not possess any atom. Hence it is either a singleton set or it is infinite. We consider also the relations between conv Open image in new window and conv G, where (G, u) is a unital lattice-ordered group with Open image in new window = Γ (G, u).

In a recent paper [CHAJDA, I.—KÜHR, J.: A non-associative generalization of MV-algebras, Math. Slovaca 57, (2007), 301–312], authors introduced and studied a non-associative generalization of MV-algebras called NMV-algebras. In contrast to MV-algebras, sections (i.e. principal filters) in NMV-algebras which are proper (i.e. are not MV-algebras), do not admit a structure of an NMV-algebra with respect to the operations defined in a natural way. The aim of the paper is to present a new class of algebras generalizing MV-algebras but sharing the above property.

The local Langlands correspondence is a conjectural connection between representations of groups G(k) for connected reductive groups G over a padic field k and certain homomorphisms (Langlands parameters) from the Galois (or Weil-Deligne group) of k into a complex Lie group G which is dual, in a certain sense, to G and which encodes the splitting structure of G over k. More introductory remarks on the local Langlands correspondence can be found in [21]. WhenG = GL1 this correspondence should reduce to local abelian class field theory. For G = GLn, the Langlands correspondence is uniquely determined by local factors [24] and was shown to exist in [23] and [25]. So far this correspondence is not completely explicit, but much progress has been made in this direction; see [9], [10], for example. For groups other than GLn or PGLn, the theory is much less advanced; new phenomena appear, arising on the arithmetic side from the difference between conjugacy and stable conjugacy and on the dual side from nontrivial monodromy of Langlands parameters. This means that a single Langlands parameter φ should determine not just one, but a finite set of representations Π(φ); these are the “L-packets” of the title. However, since local factors have not been defined in general, there is no precise characterization of an L-packet for general groups. One can, at present, only hope to define finite sets of representations Π(φ) attached to Langlands parameters φ, and show that they have properties expected (or perhaps unexpected) of L-packets. (See [14, chap. 3] for some of these properties.) One is thereby proposing a definition of local factors for the representations in the sets Π(φ) (cf. [4, chap.3]). This paper is a sequel to [14]. The aim of both papers is to verify, in an explicit and natural way, the local Langlands correspondence for the simplest kinds of non-abelian extensions of k, and the simplest kinds of

The present paper is a continuation of [2] where we deal with the duality for a multiobjective fractional optimization problem. The basic idea in [2] consists in attaching an intermediate multiobjective convex optimization problem to the primal fractional problem, using an approach due to Dinkelbach ([6]), for which we construct then a dual problem expressed in terms of the conjugates of the functions involved. The weak, strong and converse duality statements for the intermediate problems allow us to give dual characterizations for the efficient solutions of the initial fractional problem. The aim of this paper is to compare the intermediate dual problem with other similar dual problems known from the literature. We completely establish the inclusion relations between the image sets of the duals as well as between the sets of maximal elements of the image sets.

Originally I. N. Vekua's theory of generalized analytic functions dealt only with linear systems of partial differential equations in the plane. The present paper shows why I. N. Vekua's ideas are also fruitful for the solution of linear and non-linear partial differential equations in higher dimensions. One of the highlights of the theory of generalized analytic functions in the plane is the reduction of boundary value problems for general (linear or nonlinear) equations to boundary value problems for holomorphic functions using the well-known weakly singular and strongly singular 𝑇- and П-operators, respectively. The present paper is mainly aimed at reducing boundary value problems in higher dimensions to boundary value problems for monogenic functions.

This paper investigates the singular Dirichlet problem –𝑢″ = 𝑓(𝑡, 𝑢, 𝑢′), 𝑢(0) = 0, 𝑢(𝑇) = 0, where 𝑓 satisfies the Carathéodory conditions on the set and . The function 𝑓(𝑡, 𝑥, 𝑦) can have time singularities at 𝑡 = 0 and 𝑡 = 𝑇 and space singularities at 𝑥 = 0 and 𝑦 = 0. The existence principle for the above problem is given and its application is presented here. The paper provides conditions which guarantee the existence of a solution which is positive on (0; T) and which has the absolutely continuous first derivative on [0, 𝑇].

In this paper, necessary and sufficient conditions for the oscillation and asymptotic behaviour of solutions of the second order neutral delay differential equation (NDDE) $$\left[ {r(t)(y(t) - p(t)y(t - \tau ))'} \right]^\prime + q(t)G(y(h(t))) = 0$$ are obtained, where q, h ∈ C([0, ∞), ℝ) such that q(t) ≥ 0, r ∈ C (1) ([0, ∞), (0, ∞)), p ∈ C ([0, ∞), ℝ), G ∈ C (ℝ, ℝ) and τ ∈ ℝ+. Since the results of this paper hold when r(t) ≡ 1 and G(u) ≡ u, therefore it extends, generalizes and improves some known results.

In this paper, the near-field approximation of the acoustic Green's function in a two-layer waveguide is constructed by using a variation of the method of Ahluwalia and Keller (1). The relation between the con- structed multiple-scattering representation (suitable for near-field) and the Hankel transform representation (suitable for mid-range) is also discussed in this paper. The construction scheme presented in this paper can be general- ized for an N-layer waveguide. In this paper, we show how to construct acoustic Green's functions for a water column with fluid-like basement atop a rigid rockbed. The main interest is to obtain a representation of the acoustic Green's function which is valid in the near field. It is hoped with a near field Green's function, we will be able to solve the unknown object, inverse problem for an object submerged in an ocean with a layer of fluid-like sediment atop rigid rock, much in the same way as in (5), (3) for the completely reflecting seabed. In these papers, the method of integral equations is used, hence the need for an accurate near-field approximation. An alternate method which could also make use of an accurate near-field Green's function is the method of complete families of solutions. The idea of this method is discussed in (2) by Bergman and Schier, but goes back much farther. This method has been used eectively

In this paper, we study the asymptotic behavior of the solutions of the one-dimensional Cauchy problem in Timoshenko system with thermal effect. The heat conduction is given by the type III theory of Green and Naghdi. We prove that the dissipation induced by the heat conduction alone is strong enough to stabilize the system, but with slow decay rate. To show our result, we transform our system into a first order system and, applying the energy method in the Fourier space, we establish some pointwise estimates of the Fourier image of the solution. Using those pointwise estimates, we prove the decay estimates of the solution and show that those decay estimates are very slow and, in the case of nonequal wave speeds, are of regularity-loss type. This paper solves the open problem stated in [10] and shows that the stability of the solution holds without any additional mechanical damping term.

The applications of q-calculus in the approximation theory is a very interesting area of research in the recent years, several new q-operators were introduced and their behaviour were discussed by many researchers. This paper is the extension of the paper [15], in which Durrmeyer type generalization of q-Baskakov-Stancu type operators were discussed by using the concept of q-integral operators. Here, we propose to study the Stancu variant of q-Baskakov-Stancu type operators. We establish an estimate for the rate of convergence in terms of modulus of continuity and weighted approximation properties of these operators.

In this paper we establish for a bounded linear operator defined on a Banach space several sufficient and necessary conditions for which property (gaw) holds. In this work, we consider commutative perturbations by algebraic operator and quasinilpotent operator for T ∈ B(X ) such that T * satisfies property (gaw). We prove that if A is an algebraic and T ∈ PS(X ) is such that AT = TA, then ƒ(T * + A*) satisfies property (gaw) for every ƒ ∈ Hc(σ(T + A)). Moreover, we show that if Q is a quasi-nilpotent operator and T ∈ PS(X ) is such that TQ = QT, then ƒ(T * + Q*) satisfies the property (gaw) for every ƒ ∈ Hc(σ(T +Q)). At the end of this paper, we apply the obtained results to a number of subclasses of PS(X ).

In this paper, we mainly derive the general solutions of two systems of minus partial ordering equations over von Neumann regular rings. Meanwhile, some special cases are correspondingly presented. As applications, we give some necessary and sufficient conditions for the existence of solutions. It can be seen that some known results can be regarded as the special cases of this paper.

The main aim of this paper is to state recent results in Riemannian geometry obtained by the existence of a Riemannian map between Riemannian manifolds and to introduce certain geometric objects along such maps which allow one to use the techniques of submanifolds or Riemannian submersions for Riemannian maps. The paper also contains several open problems related to the research area.

Let R be a commutative Noetherian ring and let M be a finitely generated R-module. Let X = SpecR(M) be the topological space with Zariski topology. Our main goal in this paper is to describe the connectedness dimension of X in terms of Krull dimension of some quotient of M and prove that c(Spec R (M)) = c(Supp(M)). Throughout this paper R denotes a commutative ring with an identity and the notation "‰" denotes the strict inclusion. Let M be an R-module. Then a proper submodule N of M is said to be prime if for any r 2 R and any m 2 M with rm 2 N we have m 2 N or r 2 (N :R M). Further, the spectrum of M is denoted by Spec R (M) and defined by

The paper presents a new type of density topology on the real line generated by the pointwise convergence, similarly to the classical density topology which is generated by the convergence in measure. Among other things, this paper demonstrates that the set of pointwise density points of a Lebesgue measurable set does not need to be measurable and the set of pointwise density points of a set having the Baire property does not need to have the Baire property. However, the set of pointwise density points of any Borel set is Lebesgue measurable.