bluuebunny/crossref_metadata_2025_split huggingface dataset:
Meromorphic starlike univalent functions
Authors: Anh V. V. , Tuan P. D. 
Published: April 2009

Let B be the class of functions ω(z) regular in |z| < 1 and satisfying ω(0) = 0, |ω(z)|<1 in |z|<1. We denote by P(A, B), −1 ≤ B < A ≤1, the class of functions p(z) = l+p1z+… regular in |z| < 1 and such that p(z) = [1+Aω(z)]/[1+Bω(z)] for some ω(z) ∈ Β. This paper establishes sharp lower and upper bounds on |z| = r<1 for the functionalwhere p(z) varies in P(A, B). The results are then used to study certain geometric properties of the corresponding class of meromorphic starlike univalent functions
Length and area inequalities for the derivative of a bounded and holomorphic function
Authors: Yamashita Shinji 
Published: April 2009

The Schwarz-Pick lemma,for f analytic and bounded, |f|<1, in the disk |z|<1, is refined:where Φ(z, r) is a quantity determined by the non-Euclidean area of the image ofand ψ(z, r) is that determined by the non-Euclidean length of the image of the boundary of D(z, r). The multiplicities in both images by f are not counted.
Topological categories with many symmetric monoidal closed structures
Authors: Kelly G.M. , Rossi F. 
Published: April 2009

It would seem from results of Foltz, Lair, and Kelly that symmetric monoidal closed structures, and even monoidal biclosed ones, are quite rare on one-sorted algebraic or essentially-algebraic categories. They showed many such categories to admit no such structures at all, and others to admit only one or two; no such category is known to admit an infinite set of such structures.Among concrete categories, topological ones are in some sense at the other extreme from essentially-algebraic ones; and one is led to ask whether a topological category may admit many such structures. On the category of topological spaces itself, only one such structure - in fact symmetric - is known; although Greve has shown it to admit a proper class of monoidal closed structures. One of our main results is a proof that none of these structures described by Greve, except the classical one, is biclosed.Our other main result is that, nevertheless, there exist topological categories (of quasi-topological spaces) which admit a proper class of symmetric monoidal closed structures. Even if we insist (like most authors) that topological categories must be wellpowered, we can still exhibit ones with more such structures than any small cardinal.
On the volume and projection of convex sets containing no lattice points
Authors: Scott P. R. 
Published: April 2009

A convex body K in En containing no lattice points, has one-deimensional projections of lengths X1, X2, …, Xn on the coordinate axes. We show that for n ≥ 2 and 1 ≤ Xi ≤ n/(n−1) (1 ≤ i ≤ n),and this bound can not be improved.
Torsion in the additive group of relatively free Lie rings
Authors: Drensky Vesselin 
Published: April 2009

Let L = L(X) be the free Lie ring of countable rank and let p be prime. Then L(Vp) = L/[(L')p, L] is the relatively free ring for the variety of Lie rings Vp = [Np−1A, E] and Vp is defined by the identityThe purpose of this note is to establish that there exist elements of order p in the additive group of L(Vp). Previously, the existence of p-torsion was proved by Kuz'min for p = 2 only. Similar results were obtained for varieties of groups by Gupta when p = 2 and by Stöhr when p = 3.
Fields countably generated over a proper subfield
Authors: Deveney James K. , Yanik Joe 
Published: April 2009

For an arbitrary field K there are two related questions that can be asked:(1) Is there a proper subfield, L, of K such that K is countably generated over L?(2) Given a proper subfield M of K is there a proper subfield, L, of K containing M such that K is countably generated over L?We give an affirmative answer to (1) in characteristic p ≠ 0 and provide counterexamples to (2) for arbitrary characteristic ≠ 2.
Bounded measurable simultaneous monotone approximation
Authors: Sahab Salem M.A. 
Published: April 2009

Let X = [a, b] be a closed bounded real interval. Let B be the closed linear space of all bounded real valued functions defined on X, and let M ⊆ B be the closed convex cone consisting of all monotone non-decreasing functions on X. For f, g ∈ B and a fixed positive w ∈ B, we define the so-called best L∞-simultaneous approximant of f and g to be an element h* ∈ M satisfyingfor all h ∈ M, whereWe establish a duality result involving the value of d in terms of f, g and w only.If in addition f, g and w are continuous, then some characterisation results are obtained.
Laurent expansion of Dirichlet series
Authors: Balakrishnan U. 
Published: April 2009

Let 〈an〉 be an increasing sequence of real numbers and 〈bn a sequence of positive real numbers. We deal here with the Dirichlet series and its Laurent expansion at the abscissa of convergence, λ, say. When an and bn behave likeas N → ∞, where P2(x) is a certain polynomial, we obtain the Laurent expansion of f (s) at s = λ, namelywhere P1(x) is a polynomial connected with P2(x) above. Also, the connection between P1 and P2 is made intuitively transparent in the proof.
Wreath decompositions of finite permutation groups
Authors: Kovács L. G. 
Published: April 2009

There is a familiar construction with two finite, transitive permutation groups as input and a finite, transitive permutation group, called their wreath product, as output. The corresponding ‘imprimitive wreath decomposition’ concept is the first subject of this paper. A formal definition is adopted and an overview obtained for all such decompositions of any given finite, transitive group. The result may be heuristically expressed as follows, exploiting the associative nature of the construction. Each finite transitive permutation group may be written, essentially uniquely, as the wreath product of a sequence of wreath-indecomposable groups, amid the two-factor wreath decompositions of the group are precisely those which one obtains by bracketing this many-factor decomposition.If both input groups are nontrivial, the output above is always imprimitive. A similar construction gives a primitive output, called the wreath product in product action, provided the first input group is primitive and not regular. The second subject of the paper is the ‘product action wreath decomposition’ concept dual to this. An analogue of the result stated above is established for primitive groups with nonabelian socle.Given a primitive subgroup G with non-regular socle in some symmetric group S, how many subgroups W of S which contain G and have the same socle, are wreath products in product action? The third part of the paper outlines an algorithm which reduces this count to questions about permutation groups whose degrees are very much smaller than that of G.
On a centre-like subset of a ring without nil ideals
Authors: Nada Itzhak 
Published: April 2009

We give a new proof of the hypercentre theorem of Herstein.In [1], Herstein has defined the hypercentre of a ring R as follows:Herstein has proved:THEOREM. If R is a ring without non-zero nil ideals, thenT (R) = Z (R).
Manufacturing sequences for the Economic Lot Scheduling problem
Authors: Fitz-Gerald James M. , Billington Elizabeth J. 
Published: April 2009

In the basic Economic Lot Scheduling problem, a production schedule is required to manufacture sequentially a number of products on a single machine, with the schedule chosen to minimize set-up and inventory costs. The products suffer continuous demand, and no shortfall is allowed. A recent approach involves repetitions of a production cycle (such as ABCBC for three products A, B and C, with manufacturing times chosen to prevent shortage occurring); an exhaustive search is performed over a large set of possible cycles to discover the optimal schedule.This paper discusses the question “How many such sycles need to be examined?”, Since the answer is very relevant to practical application of the method. The case of three products is considered. Complete information is obtained for cycles up to length 12 (that is, 12 production switch overs), and partial results for longer ones. An estimate, apparently reasonable, is obtained for cycles of any length. The major trend to emerge is that surprisingly few cycles are involved.
On analytic functions with reference to the Bernardi integral operator
Authors: Reddy G. Lakshma , Padmanabhan K.S. 
Published: April 2009

Bernardi has proved that if f if starlike univalent in the uni disc E, then so is the function g given byIn the first part of the paper, we extend Bernardi's theorem to a certain class of p-valent starlike functions in E. We prove that if then g, defined byalso belongs to . In the second part of the paper we examine the converse problem for functions with negative coefficients, satisfying certain conditions.
On almost-Hermite-Fejér-interpolation: pointwise estimates
Authors: Gonska Heinz H. 
Published: April 2009

We give a brief survey of the results obtained by numerous authors in so-called almost-Hermite-Fejér-interpolation and deal mainly with new quantitative assertions.These are based upon more general theorems for certain continuous linear operators which yield estimates involving different types of moduli of continuity.Our paper shows that in the case of almost-Hermite-Fejér-interpolation the underlying general technique can be used to treat three essentially different cases: sequences of positive operators, which converge uniformly for every continuous function on [−1, 1], sequences of non-positive operators doing the same, and sequences of operators which converge on proper subspaces ofC[−1, 1] only.
Recurrence relations in a modular representation algebra
Authors: Renaud J-C. 
Published: April 2009

In 1978 Almkvist and Fossum examined the decomposition of the exterior powers of basis modules in the modular representation algebra of a cyclic group of prime order. In particular they developed an isomorphism between these exterior powers and terms of binomial coefficient type in the algebra.We derive several recurrence relations for these terms.
Paranormal operators on Banach spaces
Authors: Chourasia N.N. , Ramanujan P.B. 
Published: April 2009

In this note we show that a paranormal operator T on a Banach space satisfies Weyl's theorem. This is accomplished by showing that(i) every isolated point of its spectrum is an eigenvalue and the corresponding eigenspace has invariant complement,(ii) for α ≠ 0, Ker(T-α) ⊥ Ker (T-β) (in the sense of Birkhoff) whenever β ≠ α.
Normal Fitting classes and Hall subgroups
Authors: Cusack Elspeth 
Published: April 2009

It was shown by Bryce and Cossey that each Hall π-subgroup of a group in the smallest normal Fitting class S* necessarily lies in S*, for each set of primes π. We prove here that for each set of primes π such that |π| ≥ 2 and π′ is not empty, there exists a normal Fitting class without this closure property. A characterisation is obtained of all normal Fitting classes which do have this property.Let F be a normal Fitting class closed under taking Hall π-subgroups, in the sense of the paragraph above, and let Sπ denote the Fitting class of all finite soluble π-groups, for some set of primes π. The second main theorem is a characterisation of the groups in the smallest Fitting class containing F and Sπ in terms of their Hall π-subgroups.
Infinite series and the derived set of the aggregate of the fractional parts of its partial sums
Authors: Moorthy S. Audinarayana 
Published: April 2009

The aim of this paper is to study the relationship between the nature of an infinite series of real terms in which the general term tends to zero and the derived set (set of limit points) of the aggregate of the fractional parts of its partial sums. For all types of series (in which the nth term tends to zero) we determine the derived set.We denote by F the set of the fractional parts of the partial sums of the series, and by F′ the derived set of F. The principal results of the paper can be stated as follows:1. the series is convergent if and only if F has at most one limit point in [0, 1] or F′ ⊆ {0, 1};2. the series, if non-oscillatory, is divergent if and only if F′ = [0, 1];3. if the series is oscillatory, F′ is a closed sub-interval of [0, 1] or [0, 1] - (a, b), where (a, b) ⊊ (0, 1).
On intersecting families of finite sets
Authors: Frankl Peter 
Published: April 2009

Let F be a family of k-element subsets of an n-set, n > n0(k). Suppose any two members of F have non-empty intersection. Let τ(F) denote min|T|, T meets every member of F. Erdös, Ko and Rado proved and that if equality holds then τ(F) = 1. Hilton and Milner determined max|F| for τ(F) = 2. In this paper we solve the problem for τ(F) = 3.The extremal families look quite complicated which shows the power of the methods used for their determination.
What is the theory of shape?
Authors: Borsuk Karol , Dydak Jerzy 
Published: April 2009

This expository article on Shape Theory contains the main concepts of this theory with a formulation of the most important results of this theory and also with some open problems. The proofs are omitted, however the article gives references to the hooks and papers, in which the reader can find the proofs.For simplicity, we formulate several theorems only in the form which clearly gives their geometric sense, even if there are known more general results with rather complicated formulations. The reader more interested in details, can find them in the original papers quoted in the list of references.
On starlike functions
Authors: Gupta V.P. , Ahmad Iqbal 
Published: April 2009

Let S denote the class of functions f analytic and univalent in the open disc {z: |z| < 1} and normalized by f(0) = 0 = f′(0) − 1, and S*(α) denote the set of starlike functions of order α (0 ≤ α ≤ 1) in S. In this paper, the results of William M. Causey and William L. White [J. Math. Anal. Appl. 64 (1978), 458–466] are generalized by the following:THEOREM 1. Let f, g and h belong to S*(α), S*(λ) and S*(γ) , respectively and let F be defined bywhere a, c ∈ N. Then F belongs to S*(β) for |z| less than a suitably chosen number.THEOREM 2. Let F, g and h belong to S*(α), S*(λ) and S*(γ) , respectively and f be given by **. Then f belongs to S*(β) , for |z| less than a suitably chosen number.
Metrizable (LF)-spaces, (db)-spaces, and the separable quotient problem
Authors: Saxon Stephen A. , Narayanaswami P.P. 
Published: April 2009

The existence of metrizable (LF)-spaces was announced by Stephen A. Saxon (“Metrizable generalized (LF)-spaces”, 701–46–14), in Notices Amer. Math. Soc. 20 (1973), A–143. Elsewhere, the authors have discovered an abundant existence of metrizable and normable (generalized) (LF)-spaces, while observing that an (LF)-space is metrizable if and only if it is Baire-like. Recently, W. Robertson, I. Tweddle and F.E. Yeomans introduced the class of locally convex spaces E having the property(db) if E is the union of an increasing sequence (En) of vector subspaces, then some En is dense and barrelled.
Manifolds of smooth maps II: transversality
Authors: Nghê Truong Công 
Published: April 2009

We generalise the standard notion of transversality to maps between manifolds modelled on locally convex spaces and prove that all standard transversal theorems remain valid for this generalised notion.As first applications, we use our generalised Transversal Density Theorem to prove several simple “generic” results for local smooth maps which parallel the usual ones.
On the absolute Nörlund summability factors of a Fourier series and its conjugate series at a point
Authors: Kanno Kôsi 
Published: April 2009

The object of this paper is to give generalizations of Okuyama's Theorem [Bull. Austral. Math. Soc.12 (1975), 9–21, Tôohoku Math. J. (2) 28 (1976), 563–581] on the absolute Nörlund summability factors of a Fourier series and its conjugate series.Our theorems imply many results proved by other authors: especially Theorem 1 includes the results of Bhatt and Kishor [Indian J. Math.9 (1967), 259–267 (1968)], Dikshit [Pacific J. Math.63 (1976), 371–379], and Lal [Publ. Inst. Math. (Beograd) 20 (34) (1976), 169–178], and we can easily deduce Lal's result [Indian J. Math.16 (1974), 1–22] from our Corollary 2.
Path decompositions of digraphs
Authors: Abdul-Kader Issam 
Published: April 2009

Let G = (X, U) be a digraph of order n. P(G) denotes the minimal cardinal of a path-partition of the arcs of G.Oystein Ore, Theory of graphs (Amer. Math. Soc, Providence, Rhode Island, 1962) has proved that , where . We say that G satisfies Q if the preceeding inequality is an equality.We give some properties of the digraphs satisfying Q, and in particular the case where G is strongly connected. Then we prove that P(G) ≤ [n2/4], and that this result is the best possible. Next we exhibit the existence of digraphs with circuits such that P(G) = [n2/4].Finally we prove that if G is a strongly connected digraph of order n which satisfies Q, then there exists a strongly connected digraph H of order n + 1 having G as a sub-digraph and satisfying Q, too.
Note on asymptotic equivalence for measure differential equations Corrigendum
Authors: Rao V. Sree Hari 
Published: April 2009

The last 3 references in the author's note [1] should read as follows:[4] V. Sree Hari Rao, “On boundedness of impulsively perturbed systems”, Bull. Austral. Math. Soc. 18 (1978), 237–242.[5] V. Sree Hari Rao, “Asymptotically self invariant sets and stability of measure differential equations“, Nonlinear Anal., Theory, Methods Appl. 2 (1978), 483–489.[6] V. Sree Hari Rao, ”Note on conditionally asymptotically invariant sets“, J. Mathematical and Physical Sci. 12 (1978), 469–471.
Group extensions are quasi-simply-filtrated
Authors: Brick S.G. , Mihalik M.L. 
Published: April 2009

A finitely presented group G is quasi-simply-filtrated (abbreviated qsf) if, given a finite complex with fundamental group G, the universal cover of the complex can be “approximated” by simply connected finite complexes. This notion is a generalisation of a concept of Casson's used in the study of three-manifolds.In this paper we show that any extension of a finitely presented infinite group by a finitely presented infinite group is qsf.
The minimal number of periodic orbits of periods guaranteed in Sharkovskii's theorem: Corrigendum
Authors: Du Bau-Sen 
Published: April 2009

In Theorem 2 of [1] conclusion (c) should read:(c) lim(log[Φn(m)/(m])/m=log λn, where λn is the (unique) m→∞ positive (and the largest in absolute value) zero of the x2n+1 − x2n+1 − 1.
Blaschke-type maps and harmonic majoration on Riemann surfaces
Authors: Yamashita Shinji 
Published: April 2009

An analytic map h of type Bl from a Riemann surface R into another S, both having Greens functions, behaves well near the “boundaryr” of R. Let X stand for a family of holomorphic functions, and let f be holomorphic on S. We shall show, for several X′s, the following:(i) f ∈ X(S) ⇔ foh ⇔ X(R);‖foh‖ = ‖f‖.Use is made of harmonic majoration of subharmonic functions on R and on S.
Central automorphisms of finite groups
Authors: Curran M. J. , McCaughan D. J. 
Published: April 2009

This paper considers an aspect of the general problem of how the structure of a group influences the structure of its automorphisms group. A recent result of Beisiegel shows that if P is a p-group then the central automorphisms group of P has no normal subgroups of order prime to p. So, roughly speaking, most of the central automorphisms are of p-power order. This generalizes an old result of Hopkins that if Aut P is abelian (so every automorphisms is central), then Aut P is a p-group.This paper uses a different approach to consider the case when P is a π-group. It is shown that the central automorphism group of P has a normal. π′-subgroup only if P has an abelian direct factor whose automorphism group has such a subgroup.
A note on n-harmonic majorants
Authors: Kim Hong Oh , Lee Chang Ock 
Published: April 2009

Suppose D (υ) is the Dirichlet integral of a function υ defined on the unit disc U in the complex plane. It is well known that if υ is a harmonic function in U with D (υ) < ∞, then for each p, 0 < p < ∞, |υ|p has a harmonic majorant in U.We define the “iterated” Dirichlet integral Dn (υ) for a function υ on the polydisc Un of Cn and prove the polydisc version of the well known fact above:If υ is an n-harmonic function in Un with Dn (υ) < ∞, then for each p, 0 < p < ∞, |υ|p has an n-harmonic majorant in Un.
The Cauchy problem for a second-order nonlinear hyperbolic equation with initial data on a line of parabolicity
Authors: Rassias John M.S. 
Published: April 2009

In this paper we study the Cauchy problem for the second order nonlinear hyperbolic partial differential equationwith initial conditionswhereand |u|, |ux|, |uy| < ∞, y ≥ 0, r = r(x) ∈ C4(·), ν = ν(x) ∈ C4(·).These conditions on k, H, f, r, and ν are assumed to be satisfied in some sufficiently small neighborhood of the segment I, y = 0, in the upper half-plane y > 0This paper generalizes the results obtained by N.A. Lar'kin (Differencial'nye Uravnenija 8 (1972), 76–84), who has treated the special case H = H(x, y, u); that is, the quasi-linear hyperbolic equation (*).
Oscillations of certain partial differential equations with deviating arguments
Authors: Lalli B.S. , Yu Y.H. , Cui B.T. 
Published: April 2009

Sufficient conditions are established for the oscillation of solutions of hyperbolic equations of neutral type of the formwhere R+ = {0, ∞), Ω is a bounded domain in Rn with a piecewise smooth boundary ∂Ω.
On union-closed sets and Conway's sequence
Authors: Renaud J-C. , Fitina L.F. 
Published: April 2009

In 1991 Renaud defined a boundary function φ(n) for union-closed sets, and evaluated it to n = 17. Also in 1991, Mallows examined a sequence a(n) defined recursively by Conway in 1988.Investigation of some properties of strictly reduced ordered power sets, a class of union-closed sets, leads to the conclusion that a(n + 1) is an upper bound for φ(n), and the union-closed sets conjecture holds if the conjecture φ(n) = a(n + 1) is valid.
Implicit parabolic differential equations
Authors: Bonafede Salvatore , Marano Salvatore A. 
Published: April 2009

Let QT = ω x (0, T), where ω is a bounded domain in ℝn (n ≥ 3) having the cone property and T is a positive real number; let Y be a nonempty, closed connected and locally connected subset of ℝh; let f be a real-valued function defined in QT × ℝh × ℝnh × Y; let ℒ be a linear, second order, parabolic operator. In this paper we establish the existence of strong solutions (n + 2 ≤ p < + ∞) to the implicit parabolic differential equationwith the homogeneus Cauchy-Dirichlet conditions where u = (u1, u2, …, uh), Dxu = (Dxu1, Dxu2, …, Dxuh), Lu = (ℒu1, ℒu2, … ℒuh).
On a conjecture of Higgins
Authors: Heath Philip R. , Nickolas Peter 
Published: April 2009

In his work on a proof of Grushko's theorem by groupoid methods, Philip Higgins proved the following subgroup theorem.Theorem. Suppose that θ:G → B is a surjective map of groups, where G and B are free products and , and where θ(Gλ) = Bλ for each λ. Let H be a subgroup of G with the property that the restriction of θ to H is surjective. Then there is a free decomposition of H with θ(Hλ) = Bλ for each λ.As Higgins has noted, there is a common strategy in the proff of this theorem and in the groupoid proofs of Kurosh and Neilsen-Schreier subgroup theorems. Higgins conjectured the existence of a common generalisation of his theorem and the Kurosh theorem, proposed a plausible statement for such a result, and hinted that the common strategy of these proofs might be extended to give a proof of the conjecture. Examined at more detailed level, however, the common strategy used in the proofs of the Kurosh theorem and Higgin's theorem is seen to diverge into two strads. In this paper, it is shown that the construction entailed in these divergent approaches are in genera; incompatible. Thus any proof of Higgin's conjecture must require substantially different techniques. In particular, the proof of a theorem by Ordman that purports to affirm the conjecture is incorrect, and the approach used in his argument cannot yield a valid proof.