bluuebunny/crossref_metadata_2025 huggingface dataset:
Geometry without topology as a new conception of geometry
Authors: Rylov Yuri A.
Published: September 2002

A geometric conception is a method of a geometry construction. The Riemannian geometric conception and a new T‐geometric one are
considered. T‐geometry is built only on the basis of information included in the metric (distance between two points). Such geometric concepts as dimension, manifold, metric tensor, curve are fundamental in the Riemannian conception of geometry, and they are derivative in the T‐geometric one. T‐geometry is the simplest geometric conception (essentially, only finite point sets are investigated) and simultaneously, it is the most general one. It
is insensitive to the space continuity and has a new property: the nondegeneracy. Fitting the T‐geometry metric with the metric tensor of Riemannian geometry, we can compare geometries, constructed on the basis of different conceptions. The comparison shows that along with similarity (the same system of geodesics, the same metric) there is a difference. There is an absolute parallelism in T‐geometry, but it is absent in the Riemannian
geometry. In T‐geometry, any space region is isometrically embeddable in the space, whereas in Riemannian geometry only convex region is isometrically embeddable. T‐geometric conception appears to be more consistent logically, than the Riemannian one.
Two problems on varieties of groups generated by wreath products
Authors: Mikaelian Vahagn H.
Published: September 2002

We outline results on varieties of groups generated by Cartesian and direct wreath products of abelian groups and pose two problems related to our recent results in that direction. A few related topics are also considered.
Explicit forms of Wick tensor powers in general white noise spaces
Authors: Huang ZhiyuanHuang , Hu Xiaoshan , Wang Xiangjun
Published: September 2002

This paper is devoted to construction and investigation of
explicit forms of Wick tensor powers in general white noise
spaces. We give an extension of some objects and structure of
Gaussian analysis to the case of more general white noise measures on E* (the dual of a nuclear space E), such that the random variable 〈ω, ξ〉 is infinitely divisible distributed for any ξ ∈ E and ω ∈ E*.
Strongly exposed points in the unit ball of trace‐class operators
Authors: Nourouzi Kourosh
Published: September 2002

A theorem of Arazy shows that every extreme point of the unit ball of trace‐class operators is strongly exposed. We give this result a simpler and direct proof here.
Thermoelasticity without energy dissipation for initially stressed bodies
Authors: Wang Jun , Slattery Susan Palmer
Published: September 2002

Thermoelastic equations without energy dissipation are formulated
for a body which has previously received a large deformation and
is at nonuniform temperature. A linear theory of thermoelasticity
without energy dissipation for prestressed bodies is derived and
the uniqueness theorem for a class of mixed initial‐boundary
value problems is established.
The averaging of nonlocal Hamiltonian structures in Whitham′s method
Authors: Maltsev Andrei Ya.
Published: September 2002

We consider the m‐phase Whitham′s averaging method and propose the procedure of “averaging” nonlocal Hamiltonian structures. The procedure is based on the existence of a sufficient number of local‐commuting integrals of the system and gives the Poisson bracket of Ferapontov type for Whitham′s system. The method can be considered as the generalization of the Dubrovin‐Novikov procedure for the local field‐theoretical brackets.
Completely generalized multivalued nonlinear quasi‐variational inclusions
Authors: Liu Zeqing , Debnath Lokenath , Kang Shin Min , Ume Jeong Sheok
Published: September 2002

We introduce and study a new class of completely generalized multivalued nonlinear quasi‐variational inclusions. Using the resolvent operator technique for maximal monotone mappings, we suggest two kinds of iterative algorithms for solving the completely generalized multivalued nonlinear quasi‐variational inclusions. We establish both four existence theorems of solutions for the class of completely generalized multivalued nonlinear quasi‐variational inclusions involving strongly monotone, relaxed Lipschitz, and generalized pseudocontractive mappings, and obtain a few convergence results of iterative sequences generated by the algorithms. The results presented in this paper extend, improve, and unify a lot of results due to Adly, Huang, Jou‐Yao, Kazmi, Noor, Noor‐Al‐Said, Noor‐Noor, Noor‐Noor‐Rassias, Shim‐Kang‐Huang‐Cho, Siddiqi‐Ansari, Verma, Yao, and Zhang.
Equivalence results for discrete Abel means
Authors: Osikiewicz Jeffrey A.
Published: September 2002

We present theorems showing when the discrete Abel mean and the Abel summability method are equivalent for bounded sequences and when two discrete Abel means are equivalent for bounded sequences.
Behavior of second order nonlinear differantial equations
Authors: Ling Rina
Published: September 2002

Qualitative behavior of second order nonlinear differential equations with variable coefficients is studied. It includes properties such as positivity, number of zeroes, oscillatory behavior, boundedness and monotonicity of the solutions.
On Tucker′s key theorem
Authors: Berman Abraham , Tarsy Michael
Published: September 2002

A new proof of a (slightly extended) geometric version of Tucker′s fundamental result is given.
A note on rings of continous functions
Authors: Yang J. S.
Published: September 2002

For a topological space X, and a topological ring A, let C(X, A) be the ring of all continuous functions from X into A under the pointwise multiplication. We show that the theorem “there is a completely regular space Y associated with a given topological space X such that C(Y, R) is isomorphic to C(X, R)” may be extended to a fairly large class of topologlcal
rings, and that, in the study of algebraic structure of the ring C(X, A), it is sufficient to study C(X, R) if A is path connected.
A note on an inequality for the gamma function
Authors: Imoru Christopher Olutunde
Published: September 2002

Some inequalities for the Wallis functions are proved. The results of this paper are consequences of some characterization of convex functions. A generalization of a result of Boyd (1) and an extentlon of an inequality of Gantschi (3) are obtained.
Equivalence classes of the 3	rd Grassman space over a 5‐dimensional vector space
Authors: Singh Kuldip
Published: September 2002

An equivalence relation is defined on ΛrV, the rth Grassman space over V and the problem of the determnation of the equivalence classes defined by this relation is considered. For any r and V, the decomposable elements form an equivalence class. For r = 2, the length of the element determines the equivalence class that it is in. Elements of the same length are equivalent, those of unequal lengths are inequivalent. When r ≥ 3, the length is no longer a sufficient indicator, except when the length is one. Besides these general questions, the equivalence classes of Λ3V, when dimV = 5 are determined.
The Rayleigh quotient and dynamic programming
Authors: Bellman Richard
Published: September 2002

The purpose of this paper is to derive a nonlinear partial differential equation for which λ given by (1.3), is one value of the solution. In Section 2, we derive this equation using a straightforward dynamic programming approach. In Section 3, we discuss some computational aspects of derermining the solution of this equation. In Section 4, we show that the same method may be applied to the nonlinear characteristic value problem. In Section 5, we discuss how the method may by applied to find the higher characteristic values. In Section 5, we discuss how the same method may be applied to some matrix problems. Finally, in Section 7, we discuss selective computation.
Substitution relations for laplace transformations
Authors: Buschman R. G.
Published: September 2002

Additional results are obtained which center around expressions for the Laplace transforms of functions of the form k(t) F[g(t)]. The finite Laplace transformation is involved in a number of the formulas. Examples involving several special cases of g and k are included.
Singular perturbation for nonlinear boundary‐value problems
Authors: Ling Rina
Published: September 2002

Asymptotic solutions of a class of nonlinear boundary‐value problems are
studied. The problem is a model arising in nuclear energy distribution. For large values of the parameter, the differential equations are of the singular‐perturbation type and approximations are constructed by the method of matched asymptotic expansions.
Numerical and graphical description of all axis crossing regions for moduli 4 and 8 which occur befor 1012
Authors: Bays Carter , Hudson Richard H.
Published: September 2002

Let πb,c(x) denote the number of primes ≤x and ≡c(modb), and for positive integers x let Δb(x, c, l) = πb,c(x) − πb,l(x). Negative values of Δ4(x, 3, 1) less than 1012 occur in six widely spaced regions. The first three regions, investigated by Leech [6], Shanks [9] and Lehmer [6 ], contain only a few thousand negative values of Δ4(x, 3, 1). However, the authors [1] have recently discovered 3 new regions, the sixth occurring before 20 billion and containing more than half a billion negative values of Δ4(x, 3, 1). In this paper numerical and graphical details of all six regions are given. Moreover, new results for the modulus 8 are presented. Previously, no negative values have been found for Δ8(x, c, 1), c = 3, 5, or 7 and our search to 1012 reveals no such values for Δ8(x, 3, 1) or Δ8(x, 7, 1). For Δ8(x, 5, 1) we have discovered the first two regions of negative values. The first of these regions, beginning at x = 588067889, contains 422, 500 negative values of Δ8(x, 5, 1); the second occurs in the vicinity of 35 billion and contains more than a billion negative values of Δ8(x, 5, 1).
Principle of objectivity and classical physics
Authors: Dutta M. , Basu U.
Published: September 2002

In literature, it is generally asserted that the “principle of objectivity” is valid for constitutive equations but not valid for general field equations. In this paper, the principle of objectivity is formulated clearly to emphasize the correct significance, and necessity of the principle and to discuss its validity in physical theories. A discussion is made to show how successfully the principle of objectivity is also applicable to non‐relativistic classical physics.
Translation planes of odd order and odd dimension
Authors: Ostrom T. G.
Published: September 2002

The author considers one of the main problems in finite translation planes to be the identification of the abstract groups which can act as collineation groups and how those groups can act.

The paper is concerned with the case where the plane is defined on a vector space of dimension 2d over GF(q), where q and d are odd. If the stabilizer of the zero vector is non‐solvable, let G0 be a minimal normal non‐solvable subgroup. We suspect that G0 must be isomorphic to some SL(2, u) or homomorphic to A6 or A7. Our main result is that this is the case when d is the product of distinct primes.

The results depend heavily on the Gorenstein‐Walter determination of finite groups having dihedral Sylow 2‐groups when d and q are both odd. The methods and results overlap those in a joint paper by Kallaher and the author which is to appear in Geometriae Dedicata. The only known example (besides Desarguesian planes) is Hering′s plane of order 27 (i.e., d and q are both equal to 3) which admits SL(2, 13).
The four known biplanes with k = 11
Authors: Salwach Chester J. , Mezzaroba Joseph A.
Published: September 2002

The four known biplanes of order 9(k = 11) are described in terms of their ovals, λ‐chain structures, and automorphism groups. An exhaustive computer search for all biplanes of order 9 with certain chain structures has produced but two, one of which is new. None of these four biplanes yield the putative plane of order 10.
Smoothness properties of functions in R2(x) at certain boundary points
Authors: Wolf Edwin
Published: September 2002

Let X be a compact subset of the complex plane ℂ. We denote by R0(X) the algebra consisting of the (restrictions to X of) rational functions with poles off X. Let m denote 2‐dimensional Lebesgue measure. For p ≥ 1, let Rp(X) be the closure of R0(X) in Lp(X, dm).

In this paper, we consider the case p = 2. Let xϵ∂X be both a bounded point evaluation for R2(X) and the vertex of a sector contained in IntX. Let L be a line which passes through x and bisects the sector. For those yϵL∩X that are sufficiently near x we prove statements about |f(y) − f(x)| for all fϵR2(X).
Parameters and solutions of linear and nonlinear oscillators
Authors: Ling Rina
Published: September 2002

Relationship between existence of solutions for certain classes of nonlinear boundary value problems and the smallest or the largest eigenvalue of the corresponding linear problem is obtained. Behavior of the solutions, as the parameter increases, is also studied.
On the asymptotic events of a Markov chain
Authors: Cohn Harry
Published: September 2002

In this paper we investigate some structure properties of the tail σ‐field and the invariant σ‐field of both homogeneous and nonhomogeneous Markov chains as representations for asymptotic events, descriptions of completely nonatomic and atomic sets and global characterizations of asymptotic σ‐fields. It is shown that the Martin boundary theory can provide a unified approach to the asymptotic σ‐fields theory.
Differentials of the 2nd kind on a product surface
Authors: Wilson J. C.
Published: September 2002

This paper deals with the problems of representing an arbitrary double differential of the second kind, defined on a surface which is the topological product of two curves, in terms of the products of simple differentials of the second kind on the two curves. The curves are assumed to be non‐singular and irreducible in a complex projective 2‐space.
Weakly compactly generated Frechet spaces
Authors: Khurana Surjit Singh
Published: September 2002

It is proved that a weakly compact generated Frechet space is Lindelöf in the weak topology. As a corollary it is proved that for a finite measure space every weakly measurable function into a weakly compactly generated Frechet space is weakly equivalent to a strongly measurable function.
Sturmian theorems for systems of differential equations
Authors: Chan C. Y.
Published: September 2002

Two Sturmian theorems are established for second order linear nonhomogeneous systems of two differential equations with the use of a maximum principle. The results also hold for homogeneous systems. For illustration, an example is given.
Controllability, Bezoutian and relative primeness
Authors: Datta B. N.
Published: September 2002

Let f(x) and g(x) be two polynomials of degree n. Then it is well‐known that the Bezoutian matrix Bfg associated with f(x) and g(x) is nonsingular if and only if f(x) and g(x) are relatively prime. We give an alternative proof of this result. The proof is based on a result on controllability derived in this note.
Operator representation of weakly Cauchy sequences in projective tensor products of Banach spaces
Authors: Baker J. M.
Published: September 2002

It is shown that the above sequences always determine linear transformations and if the sequences are bounded under the least cross norm, that the transformations are continuous. Such operators are characterized to within algebraic isomorphism with the weak‐star sequential closure of the tensor product space in its second dual, and consequently certain classes of weakly sequentially complete projective tensor products are exhibited.
On the backward heat problem: evaluation of the norm of
Authors: Biollay Yves
Published: September 2002

We show in this paper that ‖Δu‖ = ‖ut‖ is bounded ∀t ≤ T(0) < T if one imposes on u (solution of the backward heat equation) the condition ‖u(x, t)‖ ≤ M. A Hölder type of inequality is also given if one supposes ‖ut(x, T)‖ ≤ K.
Peano compactifications and property S metric spaces
Authors: Dickman R. F.
Published: September 2002

Let (X, d) denote a locally connected, connected separable metric space. We say the X is S‐metrizable provided there is a topologically equivalent metric ρ on X such that (X, ρ) has Property S, i.e. for any ϵ > 0, X is the union of finitely many connected sets of ρ‐diameter less than ϵ. It is well‐known that S‐metrizable spaces are locally connected and that if ρ is a Property S metric for X, then the usual metric completion of (X, ρ) is a compact, locally connected, connected metric space, i.e. is a Peano compactification of (X, ρ). There are easily constructed examples of locally connected connected metric spaces which fail to be S‐metrizable, however the author does not know of a non‐S‐metrizable space (X, d) which has a Peano compactification. In this paper we conjecture that: If (P, ρ) a Peano compactification of (X, ρ|X), X must be S‐metrizable. Several (new) necessary and sufficient for a space to be S‐metrizable are given, together with an example of non‐S‐metrizable space which fails to have a Peano compactification.
Extensions of group retractions
Authors: Byrd Richard D. , Lloyd Justin T. , Mena Roberto A. , Teller J. Roger
Published: September 2002

In this paper a condition, which is necessary and sufficient, is determined when a retraction of a subgroup H of a torsion‐free group G can be extended to a retraction of G. It is also shown that each retraction of a torsion‐free abelian group can be uniquely extended to a retraction of its divisible closure.
A lower bound on the number of finite simple groups
Authors: Mays Michael E.
Published: September 2002

Let S(n) = |{m < n: there is a (non‐cyclic) simple group of order m}|. Investigation of known families of simple groups provides the lower bound S(n) ≫ n1/4/logn.
A critical investigation of various subclasses of functions whose real part is bounded
Authors: Bajpai S. K.
Published: September 2002

In this paper we investigate various subclasses of univalent analytic
functions. We find that many of the subclasses introduced in the recent years are no more new and infact coincide with the class due to Jakubowski. We further study the generalised Jakubowski class of univalent functions and obtain a representational formula and use it in deriving the coefficient relations for this class
Flow between caoxial rotating disks: with and without externally applied magnetic field
Authors: Bhatnagar R. K.
Published: September 2002

The problem of flow of a Rivlin‐Ericksen type of viscoelastic fluid is discussed
when such a fluid is confined between two infinite rotating coaxial disks. The governing system of a pair of non‐linear ordinary differential equation is solved by treating Reynolds number to small. The three cases discussed are: (I) one disks is held at rest while other rotates with a constant angular velocity, (ii) one disk rorates faster than the other but in the same sense and (iii) the disks rotate in opposite senses and with different angular velocities. The radial, tranverse and axial components of the velocity field are plotted for the above three cases for different values of the Reynolds number. The results obtained for a viscoelastic fluid are compared with those for a Newtonian fluid. The velocity field for case (i) is also computed when a magnetic field is applied in a direction perpendicular to the discs and the results are compared with the case when magnetic field is absent. Some interesting features are observed for a viscoelastic fluid.
On elastic waves in a medium with randomly distributed cylinders
Authors: Bose S. K. , Debnath L.
Published: September 2002

A study is made of the problem of propagation of elastic waves in a medium with a random distribution of cylinders of another material. Neglecting ‘back scattering’, the scattered field is expanded in a series of ‘orders of scattering’. With a further assumption that the n(n > 2) point correlation function of the positions of the cylinders could be factored into two point
correlation functions, the average field in the composite medium is found to be resummable, yielding the average velocity of propagation and damping due to scattering. The calculations are presented to the order of (ka) 2 for the scalar case of axial shear waves in the composite material. Several limiting cases of interest are recovered.
Summability of alterations of convergent series
Authors: Keagy T. A.
Published: September 2002

The effect of splitting, rearrangement, and grouping series alterations on the summability of a convergent series by ℓ − ℓ and cs − cs matrix methods is studied. Conditions are determined that guarantee the existence of alterations that are transformed into divergent series and into series with preassigned sums.
Semilocal analysis of equations with smooth operators
Authors: Miel George J.
Published: September 2002

Recent work on semilocal analysis of nonlinear operator equations is
informally reviewed. A refined version of the Kantorovich theorem for Newton′s method, with new error bounds, is presented. Related topics are briefly surveyed.
Determination of the response of a class of nonlinear time invariant systems
Authors: Karmakar Sudhangshu B.
Published: September 2002

This paper illustrates by means of a simple example a new approach for the determination of the time domain response of a class of nonlinear systems. The system under investigation is assumed to be described by a nonlinear differential equation with forcing term. The response of the system is first obtained in terms of the input in the form of a Volterra functional
expansion. Each of the components in the expansion is first transformed into a multidimensional frequency domain and then to a single dimensional frequency domain by the technique of association of variables. By taking into consideration the conditions for the rapid convergence of the functional expansion the response of the system in the frequency domain can effectively be obtained by taking only the first few terms of the expansion. Time domain response is then
found by inverse Laplace transform.
Partial henselizations
Authors: Sheets Robert W.
Published: September 2002

We define and note some properties of kH‐pairs (k Henselian pairs), kN‐pairs, and kN′‐pairs. It is shown that the 2‐Henselization and the 3‐ Henselization of a pair exist. Characterizations of quasi‐local 2H‐pairs are given, and an equivalence to the chain conjecture is proved.
A generalization of the dichromatic polynomial of a graph
Authors: Farrell E. J.
Published: September 2002

The Subgraph polynomial fo a graph pair (G, H), where H⫅G, is defined. By assigning particular weights to the variables, it is shown that this polynomial
reduces to the dichromatic polynomial of G. This idea of a graph pair leads to a dual generalization of the dichromatic polynomial.
Influence of wall waviness on friction and pressure drop in channels
Authors: Vajravelu K. , Nayfeh Ali H.
Published: September 2002

An attention has been given to investigate the flow behavior of an
incompressible viscous fluid confined in horizontal wavy channels and set in motion due to the movement of the upper wall and the pressure differences. The governing equations have been solved analytically as well as numerically subject to the relevant boundary conditions by assuming that the solution consists of two parts: a mean part and a disturbance or perturbed part. For small and moderate Reynolds numbers, the analytical solution for the perturbed part has been found to be in good agreement with the numerical one. The effects of Reynolds number, the pressure gradient parameter, and the undulation wavenumber on friction and pressure drop are found to be quite significant. In addition to the flow behavior for both long and short waves and for large Reynolds numbers, the effect of the wall waviness on friction and pressure drop has been examined for
any arbitrary amplitude of the wavy wall.
Semigroup structure underlying evoluations
Authors: Parker G. Edgar
Published: September 2002

A member of a class of evolution systems is defined by averaging a one parameter family of invertible transformations G with a semigroup T. The resulting evolution system, U(t, s) = G(t)T(t − s)G(s)−1, preserves continuity and strong continuity, and in case G is a linear family, may have an identifiable generator and resolvent both of which are constructed from T. Occurrences of the class of evolutions are given to show possible applications.
Solutions of singular integral equations
Authors: Ling Rina
Published: September 2002

Qualitative behavior of solutions of possibly singluar integral equations is studied. It includes properties such as positivity, boundedness and monotonicity of the solutions of the infinite interval.
Generalizations of p‐valent functions via the hadamard product
Authors: Soni Anil K.
Published: September 2002

The classes of univalent prestarlike functions Rα, α ≥ −1, of Ruscheweyh [1] and a certain generalization of Rα were studied recently by Al‐Amiri [2]. The author studies, among other things, the classes of p‐valent functions R(α + p − 1) where p is a positive integer and α is any integer with α + p > 0. The author shows in particular that R(α + p) ⊂ R(α + p − 1) and also obtains the radius of R(α + p) for the class R(α + p − 1).
On the asymptotic Bieberbach conjecture
Authors: Alves Mauriso , Cavalcante Armando J. P.
Published: September 2002

The set S consists of complex functions f, univalent in the open unit disk, with f(0) = f′(0) − 1 = 0. We use the asymptotic behavior of the positive semidefinite FitzGerald matrix to show that there is an absolute constant N0 such that, for any with |a3| = 2.58, we have |an| < n for all n > N0.
Sums of distances between points of a sphere
Authors: Harman Glyn
Published: September 2002

Given N points on a unit sphere in k + 1 dimensional Euclidean space, we obtain an upper bound for the sum of all the distances they determine which improves upon earlier work by K. B. Stolarsky when k is even. We use his method, but derive a variant of W. M. Schmidt′s results for the discrepancy of spherical caps which is more suited to the present application.
On the Hardy‐Littlewood maximal theorem
Authors: Yamashita Shinji
Published: September 2002

The Hardy‐Littlewood maximal theorem is extended to functions of class PL in the sense of E. F. Beckenbach and T. Radó, with a more precise expression of the absolute constant in the inequality. As applications we deduce some results on hyperbolic Hardy classes in terms of the non‐Euclidean hyperbolic distance in the unit disk.
Distributional and entire solutions of linear functional differential equations
Authors: Wiener Joseph
Published: September 2002

A unified approach to the study of generalized‐function and entire solutions to linear functional differential equations with polynomial coefficients is suggested.
A direct extension of Meller′s calculus
Authors: Koh E. L.
Published: September 2002

This paper extends the operational calculus of Meller for the operator to the case where α ∈ (0, ∞). The development is àla Mikusinski calculus and uses Meller′s convolution process with a fractional derivative operator.
Translation planes of dimension two and characteristic two
Authors: Johnson N. L. , Ostrom T. G.
Published: September 2002

This article discusses translation planes of dimension two and characteristic
two. Let G be a subgroup of the linear translation complement of such a plane π. The nature of G and its possible action on π are investigated. This continues previous work of the authors. It is shown that no new groups occur.
Generalized contraction principle
Authors: Chatterjee Dipak
Published: September 2002

Fixed point theorems are proved for contraction maps on M‐convex spaces.
A special relativistic heat engine
Authors: Cariens William S.
Published: September 2002

This paper offers a marriage of concepts from both classsical thermodynamics and special relativity, thus forming a new part of modern thermodynamics. The
main concepts taken from themodynamics and special relativity are those of a heat engine and E = mc2 respectively. Central to understanding the operation of this relativistic heat engine is the fact that upon heating a mass, its rest mass increases! This concept is nonexistent in classical thermodynamics. An increase in rest mass means that both the internal energy of a mass and its macroscopic kinetic energy increase!!!

Thus, it is seen that special relativity provides a way to upgrade immediately part of a low form of energy, heat, into a high quality energy, macroscopic kinetic energy. This was the genesis of this engine.

Here is the engine′s operation: Accelerate a mass to a high speed. At that speed add heat from a comoving heat reservoir, thus increasing the kinetic energy of the mass. After heating, slow the “heavier” mass down to its initial speed. More work is seen to be produced during the last process than was absorbed during acceleration. Next, cool the mass to complete the cycle.

The efficiency of this engine is derived, and seen to be analogous to the corresponding Carnot equation.
A Hille‐Wintner type comparison theorem for second order difference equations
Authors: Hooker John W.
Published: September 2002

For the linear difference equation

urn:x-wiley:01611712:media:ijmm407243:ijmm407243-math-0001

,
a non‐oscillation comparison theorem given in terms of the coefficients cn and the series , has been proved.
Univalent functions defined by Ruscheweyh derivatives
Authors: Shukla S. L. , Kumar Vinod
Published: September 2002

We study some radii problems concerning the integral operator

urn:x-wiley:01611712:media:ijmm670460:ijmm670460-math-0001

for certain classes, namely Kn and Mn(α), of univalent functions defined by Ruscheweyh derivatives. Infact, we obtain the converse of Ruscheweyh′s result and improve a result of Goel and Sohi for complex γ by a different technique. The results are sharp.
Infinite matrices and absolute almost convergence
Authors: Mursaleen
Published: September 2002

In 1973, Stieglitz [5] introduced a notion of FB‐Convergence which provided a wide generalization of the classical idea of almost convergence due to Lorentz [1]. The concept of strong almost convergence was introduced by Maddox [3] who later on generalized this concept analogous to Stieglitz′s extension of almost convergence [4]. In the present paper we define absolute FB‐Convergence which naturally emerges from the concept of FB‐Convergence.
A characterization of the desarguesian planes of order q2 by SL(2, q)
Authors: Foulser D. A. , Johnson N. L. , Ostrom T. G.
Published: September 2002

The main result is that if the translation complement of a translation plane of order q2 contains a group isomorphic to SL(2, q) and if the subgroups of order q are elations (shears), then the plane is Desarguesian. This generalizes earlier work of Walker, who assumed that the kernel of the plane contained GF(q).
Modulational stability of Korteweg‐de Vries and Boussinesq wavetrains
Authors: Shivamoggi Bhimsen K. , Debnath Lokenath
Published: September 2002

The modulational stability of both the Korteweg‐de Vries (KdV) and the
Boussinesq wavetrains is investigated using Whitham′s variational method. It is shown that both KdV and Boussinesq wavetrains are modulationally stable. This result seems to confirm why it is possible to transform the KdV equation into a nonlinear Schrödinger equation with a repulsive potential. A brief discussion of Whitham′s variational method is included to make the paper self‐contained to some extent.
Reducing increasing monotonicity of kernels
Authors: Ling Rina
Published: September 2002

Integral equations with positive increasing kernels are transformed into ones with positive decreasing kernels, and using a similar technique, more positive increasing kernels are reduced to ones with less increasing monotonicity.
An operator inequality
Authors: Siafarikas P. D.
Published: September 2002

An inequality is proved in abstract separable Hilbert space H where A and B are bounded self‐adjoint positive operators defined in H such that R(A) = R(B) and R(A) is closed.
On a non‐self adjoint eigenfunction expansion
Authors: Naylor D.
Published: September 2002

This paper develops a formula of inversion for an integral transform similar to that associated with the names of Kontorovich and Lebedev. The kernel involves the Hankel function , in which r varies over a truncated infinite interval a ≤ r < ∞, where a > 0 and the parameter k is complex. This kind of transform is useful in the investigation of functions that satisfy the Helmholtz equation and the condition of radiation.
Nonoscillation theorems for functional differential equations of arbitrary order
Authors: Graef John R. , Grammatikopoulos Myron K. , Kitamura Yuichi , Kusano Takaŝi , Onose Hiroshi , Spikes Paul W.
Published: September 2002

The authors give sufficient conditions for all oscillatory solutions of a sublinear forced higher order nonlinear functional differential equation to converge to zero. They then prove a nonoscillation theorem for such equations. A few intermediate results are also obtained.
The Serre duality theorem for Reimann surfaces
Authors: Roy Ranjan
Published: September 2002

Given a Riemann surface S, there exists a finitely generated Fuchsian group G of the first kind acting on the upper half plane U, such that S≅U/G. This isomorphism makes it possible to use Fuchsian group methods to prove theorems about Riemann surfaces. In this note we give a proof of the Serre duality theorem by Fuchsian group methods which is technically simpler than proofs depending on sheaf theoretic methods.
On an integral inequality in N‐independent variables
Authors: Akinyele Olusola
Published: September 2002

We present a new non‐linear integral inequality of the Gronwall‐Bellman‐Bihari type in n‐independent variables with application to pointwise estimates of solutions of a certain class of non‐linear hyperbolic partial differential equation.
An application of hypergeometric functions to a problem in function theory
Authors: Moak Daniel S.
Published: September 2002

In some recent work in univalent function theory, Aharonov, Friedland, and Brannan studied the series . Brannan posed the problem of determining . Brannan showed that if β ≥ α ≥ 0, and α + β ≥ 2, then (α, β) ∈ S. He also proved that (α, 1) ∈ S for α ≥ 1. Brannan showed that for 0 < α < 1 and β = 1, there exists a θ such that for k any integer. In this paper, we show that (α, β) ∈ S for α ≥ 1 and β ≥ 1.
Epis and monos which must be isos
Authors: Fieldhouse David J.
Published: September 2002

Orzech [1] has shown that every surjective endomorphism of a noetherian module is an isomorphism. Here we prove analogous results for injective endomorphisms of noetherian injective modules, and the duals of these results. We prove that every injective endomorphism, with large image, of a module with the descending chain condition on large submodules is an isomorphism, which dualizes a result of Varadarajan [2]. Finally we prove
the following result and its dual: if p is any radical then every surjective endomorphism of a module M, with kernel contained in pM, is an isomorphism, provided that every surjective endomorphism of pM is an isomorphism.
Markovian extensions and reductions of a family of σ‐algebras
Authors: Gill Jelena Bulatovic
Published: September 2002

In the first part of this paper different properties of two special realizations of a stochastic dynamic system, as well as relationships between the realization problem and a problem derived from it are investigated. In the second part, solutions of the following two problems (that follow directly from the realization problem) are given: how to find the minimal (resp. maximal) markovlan flow of information (understood as a family of σ‐algebras) that contains (resp. is contained in) given output of a system, and is such that each of these two flows of information is equally predictable by the other one.
On the asymptotic series solution of some higher order linear differential equations at turning points
Authors: Gorman Arthur D.
Published: September 2002

The Lagrange manifold (WKB) formalism enables the determination of the asymptotic series solution of second‐order “wave type” differential equations at turning points. The formalism also applies to higher order linear differential equations, as we make explicit here illustrating with some 4th order equations of physical significance.
Bounded sets in fast complete inductive limits
Authors: Kucera Jan , Bosch Carlos
Published: September 2002

Let E1 ⊂ E2 ⊂ … be a sequence of locally convex spaces with all identity maps: En → En+1 continuous and E = indlim En fast complete. Then each set bounded in E is also bounded in some En iff for any Banach disk B bounded in E and n ∈ N, the closure of B ⋂ En in B is bounded in some Em. This holds, in particular, if all spaces En are webbed.
Another note on almost continous mappings and Baire spaces
Authors: Tong Jingcheng
Published: September 2002

The following result is proved:

Let Y be a second countable, infinite topological space with an ascending chain of regular open sets. Then a topological space X is a Baire space if and only if every mapping f : X → Y is almost continuous on a dense subset of X.

It is another improvement of a theorem of Lin and Lin [2].
Internal functionals and bundle duals
Authors: Kitchen Joseph W. , Robbins David A.
Published: September 2002

If π : E → X is a bundle of Banach spaces, X compact Hausdorff, a fibered space π* : E* → X can be constructed whose stalks are the duals of the stalks of the given bundle and whose sections can be identified with the “functionals” studied by Seda in [1] and [2] or elements of the “internal dual” Mod(Γ(π), C(X)) studied by Gierz in [3]. If the given bundle is separable and norm continuous, then the fibered space π* : E* → X is actually a full bundle of locally convex topological vector spaces (Theorem 3). In the second portion of the paper two results are stated, both of them corollaries of theorems by Gierz, concerning functionals for bundles of Banach spaces which arise, in turn, from “fields of topological spaces.”
On new classes of analytic functions with negative coefficients
Authors: Owa Shigeyoshi
Published: September 2002

We introduce the classes of analytic functions with negative coefficients by using the nth order Ruscheweyh derivative. The object of the present paper is to show coefficient inequalities and some closure theorems for functions f(z) in . Further we consider the modified Hadamard product of functions fi(z) in .
Asymmetric deformation of anisotropic Porous bodies
Authors: Chakraborty Dilip , Chakraborty Amitava
Published: September 2002

A study is made of the deformation of a transversely isotropic poro‐elastic half‐space under various types of loads applied on its boundary. The axis of symmetry of the medium is not taken perpendicular (as is usually done) but parallel to the boundary plane of the semi‐space.
Finite propagation speed and kernels of strictly elliptic operators
Authors: Gurarie David
Published: September 2002

We establish estimates of the resolvent and other related kernels and discuss Lp‐theory for a class of strictly elliptic operators on Rn. The class of operators considered in the paper is of the form A0 + B with the leading elliptic part A0 and a “singular” perturbation B, whose coefficients have Lp‐type and are modeled after Schrödinger operators.
A relationship between the modified Euler method and e
Authors: Darst Richard B. , Dence Thomas P.
Published: September 2002

Approximating solutions to the differential equation dy/dx = f(x, y) where f(x, y) = y by a generalization of the modified Euler method yields a sequence of approximates that converge to e. Bounds on the rapidity of convergence are determined, with the fastest convergence occuring when the parameter value is , so the generalized method reduces to the standard modified Euler method. The situation is similarly examined when f is altered.
Two large subsets of a functional space
Authors: Cater F. S.
Published: September 2002

Let P1 denote the Banach space composed of all bounded derivatives f of everywhere differentiable functions on [0, 1] such that the set of points where f vanishes is dense in [0, 1]. Let D0 consist of those functions in P that are unsigned on every interval, and let D1 consist of those functions in P1 that vanish on dense subsets of measure zero. Then D0 and D1 are dense Gδ‐subsets of P1 with void interior. Neither D0 nor D1 is a subset of the other.
Interior and exterior solutions for boundary value problems in composite elastic and viscous media
Authors: Jain D. L. , Kanwal R. P.
Published: September 2002

We present the solutions for the boundary value problems of elasticity when a homogeneous and isotropic solid of an arbitrary shape is embedded in an infinite homogeneous isotropic medium of different properties. The solutions are obtained inside both the guest and host media by an integral equation technique. The boundaries considered are an oblong, a triaxial ellipsoid and an elliptic cyclinder of a finite height and their limiting configurations in two and three dimensions. The exact interior and exterior solutions for an ellipsoidal inclusion and its limiting configurations are presented when the infinite host medium is subjected to a uniform strain. In the case of an oblong or an elliptic cylinder of finite height the solutions are approximate. Next, we present the formula for the energy stored in the infinite host medium due to the presence of an arbitrary symmetrical void in it. This formula is evaluated for the special case of a spherical void. Finally, we analyse the change of shape of a viscous incompressible ellipsoidal region embedded in a slowly deforming fluid of a different viscosity. Two interesting limiting cases are discussed in detail.
Pseudo‐Reimannian manifolds endowed with an almost para f‐structure
Authors: Goldberg Vladislav V. , Rosca Radu
Published: September 2002

Let be a pseudo‐Riemannian manifold of signature (n + 1, n). One defines on an almost cosymplectic para f‐structure and proves that a manifold endowed with such a structure is ξ‐Ricci flat and is foliated by minimal hypersurfaces normal to ξ, which are of Otsuki′s type. Further one considers on a 2(n − 1)‐dimensional involutive distribution P⊥ and a recurrent vector field . It is proved that the maximal integral manifold M⊥ of P⊥ has V as the mean curvature vector (up to 1/2(n − 1)). If the complimentary orthogonal distribution P of P⊥ is also involutive, then the whole manifold is foliate. Different other properties regarding the vector field are discussed.
The generalized sampling theorem for transforms of not necessarily square integrable functions
Authors: Jerri A. J.
Published: September 2002

It is known that the generalized sampling theorem is valid for certain finite limit integral transforms of square integrable functions. In this note, we will extend the validity of the theorem to include transforms of absolutely integrable functions associated with differentiable kernels. In the proof, we will use the Hölder inequality and a known theorem concerning the uniform convergence of the orthogonal series to the differentiable kernel of the particular integral transform.
On the existence of tachyons in a bradyon‐dominated universe
Authors: Johri V. B. , Srivastava S. K.
Published: September 2002

In the present paper, the question has been raised as to whether tachyons
exist in our universe. The gravitational interaction of tachyons with bradyons is discussed by employing the method of geodesic deviation of a tachyon‐trajectory from a bradyon‐trajectory. It is noted that in certain cases, tachyons are attracted by bradyons, but in most cases they are repelled from bradyons. It is speculated that, due to their superluminal speed as well as gravitational repulsion, free tachyons would have fled out of this universe and inhabited a Meta‐Universe.
Holomorphic extension of generalizations of Hp functions
Authors: Carmichael Richard D.
Published: September 2002

In recent analysis we have defined and studied holomorphic functions in tubes in ℂn which generalize the Hardy Hp functions in tubes. In this paper we consider functions f(z), z = x + iy, which are holomorphic in the tube TC = ℝn + iC, where C is the finite union of open convex cones Cj, j = 1, …, m, and which satisfy the norm growth of our new functions. We prove a holomorphic extension theorem in which f(z), z ϵ TC, is shown to be extendable to a function which is holomorphic in T0(C) = ℝn + i0(C), where 0(C) is the convex hull of C, if the distributional boundary values in 𝒮′ of f(z) from each connected component of TC are equal.
Essential supremum norm differentiability
Authors: Leonard I. E. , Taylor K. F.
Published: September 2002

The points of Gateaux and Fréchet differentiability in L∞(μ, X) are obtained, where (Ω, ∑, μ) is a finite measure space and X is a real Banach space. An application of these results is given to the space B(L1(μ, ℝ), X) of all bounded linear operators from L1(μ, ℝ) into X.
Norm‐preserving L − L integral transformations
Authors: Wei Yu Chuen
Published: September 2002

In this paper we consider an L − L integral transformation G of the form , where G(x, y) is defined on D = {(x, y) : x ≥ 0, y ≥ 0} and f(y) is defined on [0, ∞). The following results are proved: For an L − L integral transformation G to be norm‐preserving, for almost all t ≥ 0 is only a necessary condition, where for each x ≥ 0. For certain G′s. for almost all t ≥ 0 is a necessary and sufficient condition for preserving the norm of certain f ϵ L. In this paper the analogous result for sum‐preserving L − L integral transformation G is proved.
Semi‐perfect and F‐semi‐perfect modules
Authors: Fieldhouse David J.
Published: September 2002

A module is semi‐perfect iff every factor module has a projective cover. A module M = A + B (for submodules A and B) is amply supplemented iff there exists a submodule A′ (called a supplement of A) of B such M = A + A′ and A′ is minimal with this property. If B = M then M is supplemented. Kasch and Mares [1] have shown that the first and last of these conditions are equivalent for projective modules. Here it is shown that an arbitrary module is semi‐perfect iff it is (amply) supplemented by supplements which have projective covers, an extension of the result of Kasch and Mares [1]. Corresponding results are obtained for F‐semi‐perfect modules.
Minimizing the presentation of a kont group
Authors: Dugopolski Mark J.
Published: September 2002

A method for calculating the fundamental group of a knot is given. This method can be used to obtain group presentations with fewer generators and relators than other methods.
About the defects of curves holomorphic in the half plane
Authors: Hossain Moqbul
Published: September 2002

A study is made on the defects of curves holomorphic in the half plane. Several results are proved.
Integral operators of certain univalent functions
Authors: Ahuja O. P.
Published: September 2002

A function f, analytic in the unit disc Δ, is said to be in the family Rn(α) if for some α(0 ≤ α < 1) and for all z in Δ, where n ϵ No, No = {0, 1, 2, …}. The The class Rn(α) contains the starlike functions of order α for n ≥ 0 and the convex functions of order α for n ≥ 1. We study a class of integral operators defined on Rn(α). Finally an argument theorem is proved.
A note on convergence of weighted sums of random variables
Authors: Wang Xiang Chen , Rao M. Bhaskara
Published: September 2002

Under uniform integrability condition, some Weak Laws of large numbers are
established for weighted sums of random variables generalizing results of Rohatgi, Pruitt and Khintchine. Some Strong Laws of Large Numbers are proved for weighted sums of pairwise independent random variables generalizing results of Jamison, Orey and Pruitt and Etemadi.
A note on the problem of finding a (3, 9)‐cage
Authors: Wong P. K.
Published: September 2002

In this paper, we discuss The poblem of finding a (3, 9)‐cage. A hamiltonian graph with girth 9 and 54 vertices is given. Except four vertices, each of
the remaining vertices of this graph has valency Three. This graph is obtained with the aid of a computer.