scholarly journals Real rectifiable currents, holomorphic chains and algebraic cycles

2021 ◽  
Vol 8 (1) ◽  
pp. 274-285
Author(s):  
Jyh-Haur Teh ◽  
Chin-Jui Yang
Keyword(s):  
Main Tool ◽  
Algebraic Cycles ◽  
Sufficient Condition ◽  
Hodge Conjecture ◽  
Positive Real ◽  
Continuity Theorem ◽  
Fundamental Properties ◽  
Rectifiable Currents ◽  
Holomorphic Chains

Abstract We study some fundamental properties of real rectifiable currents and give a generalization of King’s theorem to characterize currents defined by positive real holomorphic chains. Our main tool is Siu’s semi-continuity theorem and our proof largely simplifies King’s proof. A consequence of this result is a sufficient condition for the Hodge conjecture.

scholarly journals QUANTITATIVE APPROXIMATION PROPERTIES FOR ITERATES OF MOMENT OPERATOR

2015 ◽  
Vol 20 (2) ◽  
pp. 261-272 ◽  
Author(s):  
Carlo Bardaro ◽  
Loris Faina ◽  
Ilaria Mantellini
Keyword(s):  
Approximation Theorem ◽  
Multiplicative Group ◽  
Main Tool ◽  
Graphical Representations ◽  
Approximation Properties ◽  
Positive Real ◽  
Numerical Examples ◽  
Moment Operator

Here we state a quantitative approximation theorem by means of nets of certain modified Hadamard integrals, using iterates of moment type operators, for functions f defined over the positive real semi-axis ]0, +∞[, having Mellin derivatives. The main tool is a suitable K-functional which is compatible with the structure of the multiplicative group ]0, +∞[. Some numerical examples and graphical representations are illustrated.

scholarly journals SOME MULTIPLICITY RESULTS TO THE EXISTENCE OF THREE SOLUTIONS FOR A DIRICHLET BOUNDARY VALUE PROBLEM INVOLVING THE P-LAPLACIAN

2011 ◽  
Vol 16 (3) ◽  
pp. 390-400 ◽  
Author(s):  
Shapour Heidarkhani ◽  
Ghasem Alizadeh Afrouzi
Keyword(s):  
Boundary Value Problem ◽  
Critical Points ◽  
Dirichlet Boundary ◽  
Boundary Value ◽  
Main Tool ◽  
Dirichlet Boundary Value Problem ◽  
Positive Real ◽  
Three Solutions ◽  
Multiplicity Results ◽  
Uniformly Bounded

In this paper we prove the existence of two intervals of positive real parameters λ for a Dirichlet boundary value problem involving the p-Laplacian which admit three weak solutions, whose norms are uniformly bounded with respect to λ belonging to one of the two intervals. Our main tool is a three critical points theorem due to G. Bonanno [A critical points theorem and nonlinear differential problems, J. Global Optim., 28:249–258, 2004].

scholarly journals Efficiency and generalised convexity in vector optimisation problems

2004 ◽  
Vol 45 (4) ◽  
pp. 523-546 ◽  
Author(s):  
Pham Huu Sach ◽  
Gue Myung Lee ◽  
Do Sang Kim
Keyword(s):  
Efficient Solution ◽  
Main Tool ◽  
Equality Constraints ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Smooth Vector ◽  
Alternative Theorem ◽  
Necessary And Sufficient

AbstractThis paper gives a necessary and sufficient condition for a Kuhn-Tucker point of a non-smooth vector optimisation problem subject to inequality and equality constraints to be an efficient solution. The main tool we use is an alternative theorem which is quite different to a corresponding result by Xu.

Cardinalities of ultraproducts of finite sets

1980 ◽  
Vol 45 (3) ◽  
pp. 574-584 ◽  
Author(s):  
Sabine Koppelberg
Keyword(s):  
Main Tool ◽  
Sufficient Condition ◽  
Finite Sets ◽  
Similar Theorem

Keisler, in [1], defined a set F(D) of infinite cardinals for every ultrafilter D on a set I, and, assuming GCH, gave a sufficient condition for a set C of infinite cardinals to have the form F(D) for suitable D and I. In this paper we prove a similar theorem (Theorem 1) under considerably weaker assumptions. Our main tool is a construction of elementary end extensions of Boolean ultrapowers of ω outlined by Shelah in [6, Exercise VI.3.35]. Hence this paper will mostly be concerned with Boolean ultrapowers of ω.

scholarly journals A characterization of real holomorphic chains and applications in representing homology classes by algebraic cycles

2020 ◽  
Vol 7 (1) ◽  
pp. 93-105
Author(s):  
Jyh-Haur Teh ◽  
Chin-Jui Yang
Keyword(s):  
Complex Manifold ◽  
Algebraic Cycles ◽  
Finite Support ◽  
Locally Finite ◽  
Holomorphic Chains

AbstractWe show that a 2k-current T on a complex manifold is a real holomorphic k-chain if and only if T is locally real rectifiable, d-closed and has ℋ2k-locally finite support. This result is applied to study homology classes represented by algebraic cycles.

scholarly journals Tiling Tripartite Graphs with $3$-Colorable Graphs

10.37236/198 ◽  
2009 ◽  
Vol 16 (1) ◽  
Author(s):  
Ryan Martin ◽  
Yi Zhao
Keyword(s):  
Positive Integer ◽  
Positive Real Number ◽  
Minimum Degree ◽  
Discrete Math ◽  
The Other ◽  
Sufficient Condition ◽  
Positive Real ◽  
Tripartite Graph ◽  
Colorable Graph ◽  
Tripartite Graphs

For any positive real number $\gamma$ and any positive integer $h$, there is $N_0$ such that the following holds. Let $N\ge N_0$ be such that $N$ is divisible by $h$. If $G$ is a tripartite graph with $N$ vertices in each vertex class such that every vertex is adjacent to at least $(2/3+ \gamma) N$ vertices in each of the other classes, then $G$ can be tiled perfectly by copies of $K_{h,h,h}$. This extends the work in [Discrete Math. 254 (2002), 289–308] and also gives a sufficient condition for tiling by any fixed 3-colorable graph. Furthermore, we show that the minimum-degree $(2/3+ \gamma) N$ in our result cannot be replaced by $2N/3+ h-2$.

Algebraic Cycles in Families of Abelian Varieties

1994 ◽  
Vol 46 (06) ◽  
pp. 1121-1134 ◽  
Author(s):  
Salman Abdulali
Keyword(s):  
Abelian Varieties ◽  
Algebraic Cycles ◽  
Hodge Conjecture ◽  
Hodge Operator

Abstract If the Hodge *-operator on the L2-cohomology of Kuga fiber varieties is algebraic, then the Hodge conjecture is true for all abelian varieties.

scholarly journals Properties of a Generalized Class of Weights Satisfying Reverse Hölder’s Inequality

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
S. H. Saker ◽  
S. S. Rabie ◽  
R. P. Agarwal
Keyword(s):  
Upper Bounds ◽  
Hölder Inequality ◽  
The Self ◽  
Power Mean ◽  
Lower And Upper Bounds ◽  
Real Numbers ◽  
Positive Real ◽  
Fundamental Properties ◽  
Reverse Hölder ◽  
Special Case

In this paper, we will prove some fundamental properties of the discrete power mean operator M p u n = 1 / n ∑ k = 1 n   u p k 1 / p , for   n ∈ I ⊆ ℤ + , of order p , where u is a nonnegative discrete weight defined on I ⊆ ℤ + the set of the nonnegative integers. We also establish some lower and upper bounds of the composition of different operators with different powers. Next, we will study the structure of the generalized discrete class B p q B of weights that satisfy the reverse Hölder inequality   M q u ≤ B M p u , for positive real numbers p , q , and B such that 0 < p < q and B > 1 . For applications, we will prove some self-improving properties of weights from B p q B and derive the self improving properties of the discrete Gehring weights as a special case. The paper ends by a conjecture with an illustrative sharp example.

scholarly journals Motivic integration and projective bundle theorem in morphic cohomology

2009 ◽  
Vol 147 (2) ◽  
pp. 295-321
Author(s):  
JYH-HAUR TEH
Keyword(s):  
Algebraic Cycles ◽  
Motivic Integration ◽  
Projective Bundle ◽  
Cohomology Groups ◽  
Hodge Conjecture ◽  
Projective Varieties ◽  
Bundle Theorem

AbstractWe reformulate the construction of Kontsevich's completion and use Lawson homology to define many new motivic invariants. We show that the dimensions of subspaces generated by algebraic cycles of the cohomology groups of two K-equivalent varieties are the same, which implies that several conjectures of algebraic cycles are K-statements. We define stringy functions which enable us to ask stringy Grothendieck standard conjecture and stringy Hodge conjecture. We prove a projective bundle theorem in morphic cohomology for trivial bundles over any normal quasi-projective varieties.

Review of Hodge theory and algebraic cycles

2017 ◽  
Author(s):  
Claire Voisin
Keyword(s):  
Exact Sequence ◽  
Hodge Theory ◽  
Algebraic Cycles ◽  
Chow Groups ◽  
Hodge Conjecture ◽  
Hodge Structures ◽  
Mixed Hodge Structures ◽  
Generalized Hodge Conjecture ◽  
Cycle Classes

This chapter provides the background for the studies to be undertaken in succeeding chapters. It reviews Chow groups, correspondences and motives on the purely algebraic side, cycle classes, and (mixed) Hodge structures on the algebraic–topological side. Emphasis is placed on the notion of coniveau and the generalized Hodge conjecture which states the equality of geometric and Hodge coniveau. The chapter first follows the construction of Chow groups, the application of the localization exact sequence, the functoriality and motives of Chow groups, and cycle classes. It then turns to Hodge structures; pursuing related topics such as polarization, Hodge classes, standard conjectures, mixed Hodge structures, and Hodge coniveau.

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