bluuebunny/crossref_metadata_2025_split huggingface dataset:
A Note on Supersoluble Groups
Authors: Johnson D. L. 
Published: December 2010

Let H be a subgroup of a group G (all groups considered throughout this article are finite); then H will be called primitive if the subgroupis distinct from H. Such subgroups, which are also called meet-irreducible, arise naturally in connection with minimal permutation representations of groups and in other contexts; for example, every subgroup of a group G can be written as an intersection of primitive subgroups of G, and the set of all primitive subgroups of G is characterized by its minimality with respect to this property. While maximal subgroups are always primitive, most groups contain non-maximal subgroups which are primitive (see remark at end of article). Note that a subgroup H of an abelian group G is primitive if, and only if, G/H is cyclic of prime-power order.
Existence Theorems for Some Weak Abstract Variable Domain Hyperbolic Problems
Authors: Carroll Robert , State Emile 
Published: December 2010

In this paper we prove some existence theorems for some weak problems with variable domains arising from hyperbolic equations of the type1.1where A = {A(t)} is, for example, a family of elliptic differential operators in space variables x = (x1, …, xn). Thus let H be a separable Hilbert space and let V(t) ⊂ H be a family of Hilbert spaces dense in H with continuous injections i(t): V(t) → H (0 ≦ t ≦ T < ∞). Let V’ (t) be the antidual of V(t) (i.e. the space of continuous conjugate linear maps V(t) → C) and using standard identifications one writes V(t) ⊂ H ⊂ V‘(t).
Subgroups of HNN Groups and Groups with one Defining Relation
Authors: Karrass A. , Solitar D. 
Published: December 2010

HNN groups have appeared in several papers, e.g., [3; 4; 5; 6; 8]. In this paper we use the results in [6] to obtain a structure theorem for the subgroups of an HNN group and give several applications.We shall use the terminology and notation of [6]. In particular, if K is a group and {φi} is a collection of isomorphisms of subgroups {Li} into K, then we call the group1the HNN group with base K, associated subgroups { Li,φi(Li)} and free part the group generated by t1, t2, …. (We usually denote φi(Li) by Mi or L–i.) The notion of a tree product as defined in [6] will also be needed.
Disconjugacy Criteria for Nonselfadjoint Differential Equations of Even Order
Authors: Kreith Kurt 
Published: December 2010

Disconjugacy criteria have been established for linear selfadjoint differential equations of order 2n by Sternberg [4] and Ahlbrandt [1]. Such differential equations can be written in the form1.1where it is assumed that the coefficients are real and that Pn(x) ≠ 0. We shall be interested in nontrivial solutions v(x) of (1.1), which satisfy1.2for distinct points α and β. The smallest β> α such that (1.2) is satisfied nontrivially by a solution of (1.1), is denoted by μ1(α) and called the first conjugate point of x = α with respect to (1.1). If no such conjugate point exists we write μ1(α) = ∞, and say that (1.1) is disconjugate on [α, ∞).The principal purpose of this paper is to generalize these disconjugacy criteria to the general linear nonselfadjoint differential equation of the form1.3
Klein's Oscillation Theorem for Periodic Boundary Conditions
Authors: Howe A. 
Published: December 2010

Multiparameter eigenvalue problems for systems of linear differential equations with homogeneous boundary conditions have been considered by Ince [4] and Richardson [5, 6], and more recently Faierman [3] has considered their completeness and expansion theorems. A survey of eigenvalue problems with several parameters, in mathematics, is given by Atkinson [1].We consider the two differential equations:1a1bwhere p1’(x), q1(x), A1(x), B1(x) and p2’(y), q2(y), A2(y), B2(y) are continuous for x ∈ [a1, b1] and y ∈ [a2, b2] respectively, and p1 (x) > 0(x ∈ [a1, b1]), p2(y) > 0 (y ∈ [a2, b2]), p1(a1) = p1(b1), p2(a2) = p2(b2). The differential equations (1) will be subjected to the periodic boundary conditions.2a2bLet us consider a single differential equation
Linear Combinations of Univalent Functions with Complex Coefficients
Authors: Stump Robert K. 
Published: December 2010

Let U be the class of all normalized analytic functionswhere z ∈ E = {z : |z| < 1} and ƒ is univalent in E. Let K denote the sub-class of U consisting of those members that map E onto a convex domain. MacGregor [2] showed that if ƒ1 ∈ K and ƒ2 ∈ K and if1then F ∉ K when λ is real and 0 < λ < 1, and the radius of univalency and starlikeness for F is .In this paper, we examine the expression (1) when ƒ1 ∈ K, ƒ2 ∈ K and λ is a complex constant and find the radius of starlikeness for such a linear combination of complex functions with complex coefficients.
On Weighted Norm Inequalities for Fractional and Singular Integrals
Authors: Walsh T. 
Published: December 2010

In a recent paper [12] Muckenhoupt and Wheeden have established necessary and sufficient conditions for the validity of norm inequalities of the form ‖ |x|αTƒ ‖q ≦ C‖ |x|αƒ ‖p, where Tƒ denotes a Calderón and Zygmund singular integral of ƒ or a fractional integral with variable kernel. The purpose of the present paper is to prove, by somewhat different methods, similar inequalities for more general weight functions.In what follows, for p ≧ 1, p′ is the exponent conjugate to p, given by l/p + l/p′ = 1. Ω will always denote a locally integrable function on Rn which is homogeneous of degree 0, Ω∼ will denote a measurable function on Rn × Rn such that for each x ∈ Rn, Ω∼(x, .) is locally integrable and homogeneous of degree 0.
On Unitary Polarities of Finite Projective Planes
Authors: Kantor William M. 
Published: December 2010

A unitary polarity of a finite projective plane of order q2 is a polarity θ having q3 + 1 absolute points and such that each nonabsolute line contains precisely q + 1 absolute points. Let G(θ) be the group of collineations of centralizing θ. In [15] and [16], A. Hoffer considered restrictions on G(θ) which force to be desarguesian. The present paper is a continuation of Hoffer's work. The following are our main results.THEOREM I. Let θ be a unitary polarity of a finite projective planeof order q2. Suppose that Γ is a subgroup of G(θ) transitive on the pairs x, X, with x an absolute point and X a nonabsolute line containing x. Thenis desarguesian and Γ contains PSU(3, q).
Injective Hulls of Torsion Free Modules
Authors: Zelmanowitz J. 
Published: December 2010

In § 1, we begin with a basic theorem which describes a convenient embedding of a nonsingular left R-module into a complete direct product of copies of the left injective hull of R (Theorem 2). Several applications follow immediately. Notably, the injective hull of a finitely generated nonsingular left R-module is isomorphic to a direct sum of injective hulls of closed left ideals of R (Corollary 4). In particular, when R is left self-injective, every finitely generated nonsingular left R-module is isomorphic to a finite direct sum of injective left ideals (Corollary 6).In § 2, where it is assumed for the first time that rings have identity elements, we investigate more generally the class of left R-modules which are embeddable in direct products of copies of the left injective hull Q of R. Such modules are called torsion free, and can also be characterized by the property that no nonzero element is annihilated by a dense left ideal of R (Proposition 12).
Topics in Direct Differential Geometry
Authors: Park Ralph 
Published: December 2010

In the theory of curves, one often makes differentiability assumptions in order that analytic methods can be used. Then one tries to weaken these assumptions as much as possible. The theory of curves which is presented here uses geometric methods, such as central projection, rather than analysis. In this way, no analytic assumptions are needed and a purely geometric theory results. Since this theory is not so well known as the analytic one, I have tried to make the treatment as self-contained as possible. It is hoped that this paper will form a quick introduction for a reader who has had no previous acquaintance with the subject.We assume that our curves satisfy a condition, which we call direct differentiability. Roughly this condition is that, at each point of the curve, all the osculating spaces exist.
Basic Objects for an Algebraic Homotopy Theory
Authors: Cherenack Paul 
Published: December 2010

The purposes of this paper are:(A) To show (§§ 1, 3, 5) that some of the usual notions of homotopy theory (sums, quotients, suspensions, loop functors) exist in the category of affine k-schemes where the affine rings are countably generated.(B) By example to demonstrate some of the more geometric relations between two objects of and their quotient or to study the algebraic suspension of one of them. See §§ 2.1, 2.2, 2.3, 3.(C) To prove (§4) that the algebraic suspension (in R/) of the n-sphere is homeomorphic to the n + 1 sphere for the usual topologies.(D) To show that the algebraic loop functor is right adjoint to the algebraic suspension functor (§5).These results can be viewed as a precursor of definitions for an algebraic homotopy theory from a “geometric” point of view (rather than a more algebraic standpoint employing Galois theory [5]).
Radicals of PID's and Dedekind Domains
Authors: Propes R. E. 
Published: December 2010

The purpose of this paper is to characterize the radical ideals of principal
ideal domains and Dedekind domains. We show that if T is a
radical class and R is a PID, then T(R) is
an intersection of prime ideals of R. More specifically,
ifthen T(R) = (p1p2 … pk), where p1,
p2, … , pk are distinct primes, and where (p1p2 … Pk) denotes the principal ideal of
R generated by p1p2 …
pk. We also characterize the radical ideals of
commutative principal ideal rings. For radical ideals of Dedekind domains we
obtain a characterization similar to the one given for PID's.
Nowhere Dense Subsets of Metric Spaces with Applications to
Stone-Cech Compactifications
Authors: Porter Jack R. , Woods R. Grant 
Published: December 2010

Let X be a metric space. Assume either that
X is locally compact or that X has no
more than countably many isolated points. It is proved that if
F is a nowhere dense subset of X, then
it is regularly nowhere dense (in the sense of Katětov) and hence is
contained in the topological boundary of some regular-closed subset of
X. This result is used to obtain new properties of the
remote points of the Stone-Čech compactification of a metric space without
isolated points.Let βX denote the Stone-Čech compactification of the
completely regular Hausdorff space X. Fine and Gillman
[3] define a point p of βX
to be remote if p is not in the βX-closure
of a discrete subset of X.
The Eigenvalues of Complementary Principal Submatrices of a
Positive Definite Matrix
Authors: Thompson R. C. , Therianos S. 
Published: December 2010

Let C be an n-square Hermitian matrix,
presented in partitioned form aswhere A is a-square and B
is b-square. Let denote the eigenvalues of C, A, B,
respectively. In a recent paper [10] the following inequality
was established:1.1if1.2This inequality is a simplification and a sharpening of an inequality
established earlier in [6], and is a wide generalization of an
inequality of Aronszajn [4].
Associated Prime Divisors in the Sense of Krull
Authors: Kuntz Richard A. 
Published: December 2010

In a recent paper by Douglas Underwood [8] several definitions of “associated prime divisors” were discussed and shown to be unique. In this note we produce a fifth type, which is due to W. Krull, and is found in his classical paper [2] and further discussed by B. Banaschewski in[1].Historically this characterization considerably predates the other four definitions.Throughout this note,Rdenotes a commutative ring with unity, and all ideals and elements are assumed to be in such a ring. We shall let upper case letters, most frequently the beginning of the alphabet, denote ideals and lower case letters, elements ofR.On the whole, our terminology will be that of [9]. We do, however, take exception with [9] in two instances, viz.
Descendingly Incomplete Ultrafilters and the Cardinality of
Ultrapowers
Authors: Adler Andrew , Jorgensen Murray 
Published: December 2010

Let D be an ultrafilter on I, and let k be
a cardinal. D is said to be k-descendingly
incomplete (k-d.i.) if there exists a chain
Xα : α < k of elements of
D such that α < β →
Xα ⊆ Xβ and Xα = ϕ. Such a chain will be called a
k-chain for D. The notion of
k-descending incompleteness is due to Chang [3].In this paper we explore the relationship between the cardinality of the
ultrapower kI/D and the existence of certain
chains on D. Since we deal so much with questions of size,
we do not ordinarily make a notational distinction between a set and its
cardinality. Where such a distinction is useful, the cardinality of a set
A will be denoted by |A|.
Residue Free Differentials and the Cartier Operator for
Algebraic Function Fields of one Variable
Authors: Kodama Tetsuo 
Published: December 2010

Let K be a field of characteristic p >
0 and let A be a separably generated algebraic function
field of one variable with K as its exact constant field.
Throughout this paper we shall use the following notations to classify
differentials of A/K:D(A) : the K-module of all differentials,G(A) : the K-module of all differentials of the first
kind,R(A) : the K-module of all residue free differentials in
the sense of Chevalley [2, p. 48],E*(A) : the K-module of all pseudo-exact
differentials in the sense of Lamprecht [7, p. 363], (compare
the definition with our Lemma 8).
The Continuity of the Visibility Function on a Starshaped
Set
Authors: Beer Gerald 
Published: December 2010

The visibility function assigns to each point x of a fixed
measurable set E in a Euclidean space En the Lebesgue outer measure of
S(x), the set {y : rx + (1 — r)y ∊ E
for every r in [0, 1]}.The purpose of this paper is to determine sufficient conditions for the
continuity of the function on the interor of a starshaped set.
On Kaehler Immersions
Authors: Ogiue Koichi 
Published: December 2010

Let be an (n + p)-dimensional Kaehler manifold of constant holomorphic sectional curvature . B. O'Neill [3] proved the following result.PROPOSITION A. Let M be an n-dimensional complex submanifold immersed in . If and if the holomorphic sectional curvature of M with respect to the induced Kaehler metric is constant, then M is totally geodesic.He also gave the following example: There is a Kaehler imbedding of an w-dimensional complex projective space of constant holomorphic sectional curvature ½ into an -dimensional complex projective space of constant holomorphic sectional curvature 1. This shows that Proposition A is the best possible.
Distributional Watson Transforms
Authors: Hsu Hsing-Yuan 
Published: December 2010

All our notation is as denned in [2] with the restriction to n = 1. However, for our purposes, we introduce a sequence of norms byin It is not difficult to see that turns out to be a fundamental space.It is a well-known fact that the Watson transform and the Mellin transform are connected by the fact thatandif and only if K(s)K(l — s) = 1, where K(s) is the Mellin transform of k(x). Further, the Hankel transform and Hilbert transform can be considered as special cases of Watson transforms.
Finite p-groups with Isomorphic Subgroups
Authors: Currano John J. 
Published: December 2010

Throughout this paper, p will denote a prime and t an integer greater than 1. We consider those finite p-groups P, which satisfy the following conditions:(1.1) P has subgroups R and Q, both of index p, and there is an isomorphism φ of R onto Q which does not fix any non-identity subgroup of R setwise.
On the Uniform Approximation of Smooth Functions by Jacobi Polynomials
Authors: Prasad J. , Hayashi H. 
Published: December 2010

Let ωn(x) denote the Jacobi polynomials with the weight FunctionIf we denote the corresponding normalized Jacobi polynomials by we Have(1.1)Now letbe the nth partial sum of the Fourier series of Jacobi polynomials of a function f(x).
Majorization-Subordination Theorems for Locally Univalent Functions, II
Authors: Campbell Douglas Michael 
Published: December 2010

Let denote the set of all normalized analytic univalent functions in the open unit disc D. Let f(z), F(z) and φ(z) be analytic in |z| < r. We say that f(z) is majorized by F(z) in we say that f(z) is subordinate to F(z) in where .Let be the set of all locally univalent (f’(z) ≠ 0) analytic functions in D with order ≦α which are of the form f(z) = z +… . The family is known as the universal linear invariant family of order α [6]. A concise summary of and introduction to properties of linear invariant families which relate to the following material is contained in [1]. The present paper contains the proofs of some of the results announced in [1]
Chromatic Sums for Rooted Planar Triangulations: The Cases λ = 1 and λ = 2
Authors: Tutte W. T. 
Published: December 2010

SummaryIn this paper we derive a functional equation whose solution would give the sum of the chromatic polynomialP(M,λ) over certain classes of rooted planar mapsMcalled “ triangulations” and “near-triangulations”. For an integral colour-number λ this sum is the number of λ-coloured rooted maps of the kind considered, but the sum can also be discussed for non-integral λ.
Quotient Rings of a Class of Lattice-Ordered-Rings
Authors: Steinberg Stuart A. 
Published: December 2010

An f-ring R with zero right annihilator is called a qf-ring if its Utumi maximal left quotient ring Q = Q(R) can be made into and f-ring extension of R. F. W. Anderson [2, Theorem 3.1] has characterized unital qf-rings with the following conditions: For each q ∈ Q and for each pair d1, d2 ∈ R+ such that diq ∈ R(i) (d1q)+ Λ (d2q)- = 0, and(ii) d1 Λ d2 = 0 implies (d1q)+ Λ d2 = 0.We remark that this characterization holds even when R does not have an identity element.
Chromatic Sums for Rooted Planar Triangulations II: The Case λ = τ + 1
Authors: Tutte W. T. 
Published: December 2010

SummaryIn an earlier paper [2] we denned the chromatic sums g, q, l and h. We determined the derivatives of these sums with respect to the colour-number λ at the special values λ = 1 and λ = 2. In the present paper we find parametric equations for h, l and q in the case λ = τ + 1, where τ is the golden ratio. We obtain h, l and the basic indeterminate z explicitly in terms of the parameter u, but for q we exhibit only a cubic equation with coefficients depending on u. We obtain an exact formula for the coefficients in h by applying Lagrange's theorem to the parametric equations.
Graphs with 6-Ways
Authors: Leonard John L. 
Published: December 2010

In a finite graph with no loops nor multiple edges, two points a and b are said to be connected by an r-way, or more explicitly, by a line r-way a — b if there are r paths, no two of which have lines in common (although they may share common points), which join a to b. In this note we demonstrate that any graph with n points and 3n — 2 or more lines must contain a pair of points joined by a 6-way, and that 3n — 2 is the minimum number of lines which guarantees the presence of a 6-way in a graph of n points.In the language of [3], this minimum number of lines needed to guarantee a 6-way is denoted U(n). For the background of this problem, the reader is referred to [3].
A Generalization of Čaplygin's Inequality with Applications to Singular Boundary Value Problems
Authors: Willett D. 
Published: December 2010

Let(1.1)where pk ∈ C(α, β) and - ∞ ≦ α < β ≦ ∞ . A solution of (1.1) is a nontrivial function y ∈ Cn(α, β), a neighborhood of β is an interval of the form (γ, β), α ≦ γ < β, and a neighborhood of α is an interval of the form (α, γ), α < γ ≦ β.
A Theorem on Permutations of a Finite Field
Authors: Bruen A. , Levinger B. 
Published: December 2010

The purpose of this note is to give a new proof of a theorem of L. Carlitz [2] and R. McConnel [5]. The theorem is as follows:THEOREM 1. Let F = GF(pn) be the finite field of order q = pn and let
K — {x ∈ F|xd = 1} for some proper divisor d of q — 1.
A Technique for Studying the Boundedness and Extendability of Certain Types of Operators
Authors: Rooney P. G. 
Published: December 2010

For 1 ≦ p < ∞, μ real, let Lμ, p denote the collection of functions f, Lebesgue measurable on (0, ∞ ), and such that ‖ f ‖μP < ∞ , where(1.1)Also, if X and Y are Banach spaces, denote by [X, Y] the collection of bounded linear operators from X to Y; [X, X] denote by [X].
On the Commutant of Certain Automorphism Groups
Authors: Tam P. K. 
Published: December 2010

Let be a W*-algebra, A ( ) the group of all automorphisms of . In this paper we have determined the commutant G’ of a subgroup G of A () for certain classes of G and . The main results are as follows.Theorem 1. If G is a locally compact abelian group acting by translation on the W*-algebra L∞(G), then the commutant of a dense subgroup of G is G itself.
Kinetic Theory and Boundary Conditions for Fluids
Authors: Schnute Jon , Shinbrot Marvin 
Published: December 2010

SummaryA rigorous derivation of the molecular theory of a confined, deterministic gas is given. Then, a molecular reflection law is presented with the property that the corresponding fluid does not slip at the boundary. It is also shown that, within a certain reasonable class of reflection laws, the one we give is the only one that leads to no-slip.
The SCnP-Integral and the Pn+1-Integral
Authors: Bullen P. S. , Lee C. M. 
Published: December 2010

In [2], we have briefly described, as examples of the general theory developed there, a scale of symmetric Cesaro-Perron integrals, namely SCnP-integral for n = 1, 2, 3, … . The purpose of this paper is to consider the integrals in a greater detail.As a preliminary, we prove some lemmas, which are also interesting for their own sake, concerning the de la Vallée Poussin derivatives in Section 1, and we also state two deep theorems concerning the n-convex functions in Section 2.
Chains of Varieties
Authors: Gupta Narain , Levin Frank , Rhemtulla Akbar 
Published: December 2010

SummaryIf is a variety of groups that can be denned by n-variable laws and (m) is the variety all of whose m-generator groups are in then there corresponds the chain: (1) ≧ (2) ≧ . . . ≧ (n) = . In this paper such chains are investigated to determine which of the inclusions are proper for certain varieties . In particular the inclusions are shown to be all proper for the varieties where is the variety of nilpotent-of-class-c groups, is the abelian variety and is the variety of centre-bymetabelian groups. For the inclusions are likewise proper but for the corresponding chain is:
The G-Function of Macrae
Authors: Rush David E. 
Published: December 2010

Let R be a commutative ring with identity. A finitely generated R-module M is called a torsion module if the annihilator of M contains a non zero-divisor. In [18] MacRae proved the followingTheorem. If R is a noetherian ring then there is a map G with the following properties from the class of torsion R-modules of finite homological dimension to the set of integral invertible ideals of R.(i) If M is a finitely generated torsion R-module with homological dimension ≦ 1 then G(M) = F(M), the first Fitting ideal of M.(ii) If S is a multiplicative subset of R then G(Ms) = G(M) s.(iii) If 0 → L → M → N → 0 is an exact sequence of torsion modules of finite homological dimension then G(M) = G(L)G(N).
The Maximum Genus of Cartesian Products of Graphs
Authors: Zaks Joseph 
Published: December 2010

The maximum genus γM(G) of a connected graph G has been defined in [2] as the maximum g for which there exists an embedding h : G —> S(g), where S(g) is a compact orientable 2-manifold of genus g, such that each one of the connected components of S(g) — h(G) is homeomorphic to an open disk; such an embedding is called cellular. If G is cellularly embedded in S(g), having V vertices, E edges and F faces, then by Euler's formulaV-E + F = 2-2g.