Showing papers in "International Journal of Mathematics and Mathematical Sciences in 1978"
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TL;DR: The purpose of this paper is to demonstrate the existence of a parallel theory concerning connected nonorientable surfaces that give rise to additional knot invariants.
Abstract: Seifert (4) demonstrated that every knot can be spanned by an orlentable surface. These Seifert surfaces lead to numerous knot invari- ants. The purpose of this paper is to demonstrate the existence of a parallel theory concerning connected nonorientable surfaces. These surfaces give rise to additional knot invariants. KEY WORDS AND PHRASES. Norieable surfaces, knot invariants, crosscaps and knots. AMS(MOS) SUBJECT CLASSIFICATIONS (1970). 55A25, 57C45. Submit your manuscripts at http://www.hindawi.com Hindawi Publishing Corporation http://www.hindawi.com Volume 2014 Mathematics Journal of Hindawi Publishing Corporation http://www.hindawi.com Volume 2014 Mathematical Problems in Engineering Hindawi Publishing Corporation http://www.hindawi.com Differential Equations International Journal of Volume 2014 Applied Mathematics Journal of Hindawi Publishing Corporation http://www.hindawi.com Volume 2014 Probability and Statistics Hindawi Publishing Corporation http://www.hindawi.com Volume 2014 Journal of Hindawi Publishing Corporation http://www.hindawi.com Volume 2014 Mathematical Physics Advances in Complex Analysis Journal of Hindawi Publishing Corporation http://www.hindawi.com Volume 2014 Optimization Journal of Hindawi Publishing Corporation http://www.hindawi.com Volume 2014 Combinatorics Hindawi Publishing Corporation http://www.hindawi.com Volume 2014 International Journal of Hindawi Publishing Corporation http://www.hindawi.com Volume 2014 Operations Research Advances in
55 citations
TL;DR: In this paper, it was shown that the problem of finding solutions of the Hammersteln integral equation can be reduced to the study of the critical points of certain functional defined on L 2.
Abstract: This paper deals with the problem of finding solutions of the --._rstein integral equation. It is shown that this problem can be reduced to the study of the critical points of certain functional defined on L2(). Existence of a solution of the Hammersteln integral equation is proved. Some other related results of interest are obtained.
34 citations
TL;DR: In this paper, it was shown that the Weierstrass property on incomplete polynomials of type θ is essentially sufficient and sufficient for any θ with 0 < θ < 1.
Abstract: For any θ with 0<θ<1, it is known that, for the set of all incomplete polynomials of type θ, i.e, {p(x)=∑k=snakxk:s≥θ⋅n}, to have the Weierstrass property on [aθ,1], it is necessary that θ2≤aθ≤1. In this paper, we show that the above inequalities are essentially sufficient as well.
21 citations
TL;DR: In this article, it was shown that if G is a labeled (p,p−2) graph where p& #x2265;2 has no fixed vertices, then there exists an isomorphic embedding of G in its complement, such that ϕ has no vertices.
Abstract: The following is proved: If G is a labeled (p,p−2) graph where p≥2, then there exists an isomorphic embedding ϕ of G in its complement G¯ such that ϕ has no fixed vertices. The extension to (p,p−1) graphs is also considered.
21 citations
TL;DR: In this paper, the standard definition of a close-to-convex function involves a complex numerical factor eiβ which is on occasion erroneously replaced by 1, and explicit reasons for this fact seem to be lacking in the literature.
Abstract: The standard definition of a close-to-convex function involves a complex numerical factor eiβ which is on occasion erroneously replaced by 1. While it is known to experts in the field that this replacement cannot be made without essentially changing the class, explicit reasons for this fact seem to be lacking in the literature. Our purpose is to fill this gap, and in so doing we are lead to a new coefficient problem which is solved for n=2, but is open for n>2.
15 citations
TL;DR: In this paper, the authors studied the properties of second order nonlinear differential equations with variable coefficients, including properties such as positivity, number of zeros, oscillatory behavior, boundedness and monotonicity.
Abstract: 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.
13 citations
10 citations
TL;DR: In this article, it was shown that the limit points of the sequence δ n form a subset C ( x ), and D (x ) can be generated from C (x) in a relatively simple way.
Abstract: Some characteristic approximation properties of quadratic irrationals are studied in this paper. It is shown that the limit points of the sequence δ n form a subset C ( x ) , and D ( x ) can be generated from C ( x ) in a relatively simple way. Another proof of Lekkerkerker's theorem
is given using relations between δ n − 1 , δ n , δ n + 1 which are independent of x and n .
9 citations
TL;DR: In this article, the authors formulated a condition for functions in L1(G) which implies that their Walsh-Fourier series converges in L 1(G)-norm and obtained a Dini-Lipschitz-type theorem for L 1 (G) convergence.
Abstract: Let G denote the dyadic group, which has as its dual group the Walsh(-Paley) functions. In this paper we formulate a condition for functions in L1(G) which implies that their Walsh-Fourier series converges in L1(G)-norm. As a corollary we obtain a Dini-Lipschitz-type theorem for L1(G) convergence and we prove that the assumption on the L1(G) modulus of continuity in this theorem cannot be weakened. Similar results also hold for functions on the circle group T and their (trigonometric) Fourier series.
9 citations
TL;DR: In this article, an operational calculus for the operator B μ = t − μ D t 1 + μ D with − 1 μ ∞ was developed via the algebraic approach, and a differentiation theorem and a convolution theorem were proved.
Abstract: Recently [8], an operational calculus for the operator B μ = t − μ D t 1 + μ D with − 1 μ ∞ was developed via the algebraic approach [4], [13], [15]. This paper gives the integral transform version. In particular, a differentiation theorem and a convolution theorem are proved.
8 citations
TL;DR: In the last few years various infinite dimensional extensions to Krasnoselski's Theorem on starshaped sets (14) have been made as mentioned in this paper, and these extensions began with a paper by Edelstein and Keener (8) and have been culmdnated in the papers by Borwein and O'Brien (3)
Abstract: In the last few years various infinite dimensional extensions to Krasnoselski's Theorem on starshaped sets (14) have been made. These began with a paper by Edelstein and Keener (8) and have culmdnated in the papers by Borwein, Edelstein and O'Brien (3) (4) by Edelstein, Keener and O'Brien
TL;DR: In this article, a translation plane of even order q2 that admits GL(2,q) as a collineation group is defined and shown to be either Desarguesian, Hall or Ott-Schaeffer.
Abstract: In this article we show the following: Let π be a translation plane of even order q2 that admits GL(2,q) as a collineation group. Then π is either Desarguesian, Hall or Ott-Schaeffer.
TL;DR: In this paper, necessary and sufficient conditions for all oscillatory solutions of the equation were found for all O(n) oscillations of the solution of the O(1) equation.
Abstract: Necessary and sufficient conditions are found for all oscillatory solutions of the equation
TL;DR: In this paper, it was shown that a matrix that maps l 1 into l 1 can be obtained from any regular matrix by the deletion of rows from a matrix preserving boundedness.
Abstract: It is proved that a matrix that maps l1 into l1 can be obtained from any regular matrix by the deletion of rows. Similarly, a conservative matrix can be obtained by deletion of rows from a matrix that preserves boundedness. These techniques are also used to derive a simple sufficient condition for a matrix to sum an unbounded sequence.
TL;DR: For the class of N-homomorphism of hemirings, the fundamental homomorphism theorem for rings is not generally applicable in hemiring theory, but it is shown in this paper that the fundamental theorem is valid in the case of heirings.
Abstract: The fundamental homomorphism theorem for rings is not generally applicable in hemiring theory. In this paper, we show that for the class of N-homomorphism of hemirings the fundamental theorem is valid. In addition, the concept of N-homomorphism is used to prove that every hereditarily semisubtractive hemiring is of type (K).
TL;DR: In this article, a generalization of a result of Boyd (1) and an extentlon of an inequality of Gantschi (3) are obtained for the Wallis functions.
Abstract: 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.
TL;DR: In this paper, the author showed that a well known sufficient condition for strict cyclic linearity of a weighted shift on p is not a necessary condition for any p with p with 1/60;p<∞.
Abstract: In this paper the author shows that a well known sufficient condition for strict cycliclty of a weighted shift on ℓp is not a necessary condition for any p with 1<p<∞.
TL;DR: In this article, sufficient conditions are established for the matrix Riccati equation to have a symmetric solution on a given interval, where the criteria involve integral conditions on the coefficient matrices of the Riemannian equation.
Abstract: Sufficient conditions are established for the matrix Riccati equation to have a symmetric solution on a given interval The criteria involve integral conditions on the coefficient matrices of the Riccati equation The present results are compared with previously known results
TL;DR: A well-known result due to S. Beatty as discussed by the authors is that if α and β are positive irrational numbers satisfying α−1, then β is a positive irrational number satisfying α −1.
Abstract: A well-known result due to S. Beatty is that if α and β are positive irrational numbers satisfying α−1
TL;DR: In this paper, it was shown that a diffeomorphism of manifolds with indefinite metrics preserving degenerate r-plane sections is conformal, and a sectional curvature-preservant diffeomorphic manifold is generically an isometry.
Abstract: It is shown that (i) a diffeomorphism of manifolds with indefinite metrics preserving degenerate r-plane sections is conformal, (ii) a sectional curvature-preservlng diffeomorphism of manifolds with indefinite metrics of dimension ≥4 is generically an isometry.
TL;DR: Sturmian comparison theorems are obtained for solutions of a class of normal and singular ultrahyperbolic partial differential equations in this article, where solutions are considered which satisfy non-standard boundary conditions.
Abstract: Sturmian comparison theorems are obtained for solutions of a class of normal and singular ultrahyperbolic partial differential equations. In the singular case, solutions are considered which satisfy non-standard boundary conditions.
TL;DR: In this article, a connection between the notion of (n−2)-tightness in the sense of N.H.Kuiper and T.F.Banchoff is established.
Abstract: The purpose of this note is to establish a connection between the notion of (n−2)-tightness in the sense of N.H. Kuiper and T.F. Banchoff and the total absolute curvature of compact submanifolds-with-boundary of even dimension in Euclidean space. The argument used is a certain geometric inequality similar to that of S.S. Chern and R.K. Lashof where equality characterizes (n−2)-tightness.
TL;DR: In this paper, a sufficient condition is given for a countable discrete group G to contain a free subgroup of two generators, where the generator is a generator and the generator a generator.
Abstract: A sufficient condition is given for a countable discrete group G to contain a free subgroup of two generators.
TL;DR: In this paper, the authors give a necessary and sufficient condition for the uniqueness of the separable idempotent for a separable group ring extension of a quaternion ring.
Abstract: lqe purposes of the present paper are (i) to give a necessary and sufficient condition for the uniqueness of the separable idempotent for a separable group ring extension RG (R may be a non-commutative ring), and (2) to give a full description of the set of separable idempotents for a qua- ternion ring extension RQ over a ring R, where Q are the usual quaternions i,j,k and multiplication and addition are defined as quaternion algebras over a field. We shall show that RG has a unique separable idempotent if and only if G is abelian, that there are more than one separable idempotents for a separable quaternion ring RQ, and that RQ is separable if and only if 2 is invertible in
TL;DR: In this article, the characterizations of the complete residue system mod is dealt with, where G is any n×n matrix, in the ring of n × n matrices.
Abstract: This paper deals with the characterizations of the complete residue system mod. G, where G is any n×n matrix, in the ring of n×n matrices.
TL;DR: In this paper, a theory of the generation and propagation of the two and the three dimensional tsunamis in a shallow running ocean due to the action of an arbitrary ocean floor or ocean surface disturbance is presented.
Abstract: A theory is presented of the generation and propagation of the two and the three dimensional tsunamis in a shallow running ocean due to the action of an arbitrary ocean floor or ocean surface disturbance. Integral solutions for both two and three dimensional problems are obtained by using the generalized Fourier and Laplace transforms. An asymptotic analysis is carried out for the investigation of the principal features of the free sur- face elevation. It is found that the propagation of the tsunamis depends on the relative magnitude of the given speed of the running ocean and the wave speed of the shallow ocean. When the speed of the running ocean is less than the speed of the shallow ocean wave, both the two and the three dimensional
TL;DR: In this article, the general solution of scalar, first-order differential equations is obtained using variation of parameters with asymptotic series and the theory of partial differential equations.
Abstract: In this paper we obtain the general solution of scalar, first-order differential equations. The method is variation of parameters with asymptotic series and the theory of partial differential equations.
TL;DR: In this article, it was shown that the set of points in the unit interval which are not midway be- tween two distinct Cantor ternary points is preclsely the subset of non-endpoints.
Abstract: A non-endpoint of the Cantor ternary set is any Cantor point which is not an endpoint of one of the remaining closed intervals obtained in the usual construction process of the Cantor ternary set in the unit interval. It is shown that the set of points in the unit interval which are not midway be- tween two distinct Cantor ternary points is preclsely the set of Cantor non- endpoints. It is also shown that the generalized Cantor set C%, for 1/3<%<1, has void intersection with its set of midpoints obtained from distinct members of C%.
TL;DR: In this article, the authors define Riemann integrabillty for real valued functions defined on a compact metric space accompanied by a finite Borel measure, and prove that a bounded function is RiemANN integrable if and only if its set of points of discontinuity has measure zero.
Abstract: In this note we define Riemann integrabillty for real valued functions defined on a compact metric space accompanied by a finite Borel measure If the measure of each open ball equals the measure of its corresponding closed ball, then a bounded function is Riemann integrable if and only if its set of points of discontinuity has measure zero
TL;DR: In this article, a new proof of a (slightly extended) geometric version of Tucker's fundamental result is given, which is a geometric extension of the fundamental result of this article.
Abstract: A new proof of a (slightly extended) geometric version of Tucker's fundamental result is given.