scholarly journals Forbidden Hypermatrices Imply General Bounds on Induced Forbidden Subposet Problems

2017 ◽  
Vol 26 (4) ◽  
pp. 593-602 ◽  
Author(s):  
ABHISHEK METHUKU ◽  
DÖMÖTÖR PÁLVÖLGYI
Keyword(s):  
Higher Dimensional ◽  
Image Position

We prove that for every posetP, there is a constantCPsuch that the size of any family of subsets of {1, 2, . . .,n} that does not containPas an induced subposet is at most$$C_P{\binom{n}{\lfloor\gfrac{n}{2}\rfloor}},$$settling a conjecture of Katona, and Lu and Milans. We obtain this bound by establishing a connection to the theory of forbidden submatrices and then applying a higher-dimensional variant of the Marcus–Tardos theorem, proved by Klazar and Marcus. We also give a new proof of their result.

scholarly journals Functional Imaging with Higher-Dimensional Electrical Data Sets

2018 ◽  
Vol 26 (6) ◽  
pp. 18-27 ◽  
Author(s):  
P. De Wolf ◽  
Z. Huang ◽  
B. Pittenger ◽  
A. Dujardin ◽  
M. Febvre ◽  
...  
Keyword(s):  
Functional Imaging ◽  
Data Sets ◽  
Higher Dimensional ◽  
Image Position ◽  
Electrical Data

Abstract

On Certain Functional Identities in EN

1971 ◽  
Vol 23 (2) ◽  
pp. 315-324 ◽  
Author(s):  
A. McD. Mercer
Keyword(s):  
Euclidean Space ◽  
Taylor Series ◽  
Dimensional Space ◽  
The Real ◽  
Higher Dimensional ◽  
Isolated Points ◽  
Functional Identities ◽  
Image Position ◽  
Special Case ◽  
Real Euclidean Space

1. If f is a real-valued function possessing a Taylor series convergent in (a — R, a + R), then it satisfies the following operational identity1.1in which D2 = d2/du2. Furthermore, when g is a solution of y″ + λ2y = 0 in (a – R, a + R), then g is such a function and (1.1) specializes to1.2In this note we generalize these results to the real Euclidean space EN, our conclusions being Theorems 1 and 2 below. Clearly, (1.2) is a special case of (1.1) but in higher-dimensional space it is of interest to allow g, now a solution of1.3to possess singularities at isolated points away from the origin. It is then necessary to consider not only a neighbourhood of the origin but annular regions also.

scholarly journals ESTIMATES FOR MARCINKIEWICZ INTEGRALS IN BMO AND CAMPANATO SPACES

2007 ◽  
Vol 49 (2) ◽  
pp. 167-187 ◽  
Author(s):  
GUOEN HU ◽  
YAN MENG ◽  
DACHUN YANG
Keyword(s):  
Regularity Condition ◽  
Mean Value ◽  
Marcinkiewicz Integral ◽  
Degree Zero ◽  
Marcinkiewicz Integrals ◽  
Almost Everywhere ◽  
Higher Dimensional ◽  
Lusin Area Integral ◽  
Image Position ◽  
Marcinkiewicz Integral Operator

AbstractIn this paper, the authors consider the behavior on BMO($\mathbb R^n$) and Campanato spaces for the higher-dimensional Marcinkiewicz integral operator which is defined by where Ω is homogeneous of degree zero, has mean value zero and is integrable on the unit sphere. Under certain weak regularity condition on Ω, the authors prove that if f belongs to BMO($\mathbb R^n$) or to a certain Campanato space, then [μΩ(f)]2 is either infinite everywhere or finite almost everywhere, and in the latter case, some kind of boundedness is also obtained. The corresponding Lusin area integral is also considered.

Periodic solutions of higher-dimensional discrete systems

2004 ◽  
Vol 134 (5) ◽  
pp. 1013-1022 ◽  
Author(s):  
Zhan Zhou ◽  
Jianshe Yu ◽  
Zhiming Guo
Keyword(s):  
Positive Integer ◽  
Critical Point ◽  
Periodic Solutions ◽  
Critical Point Theory ◽  
Discrete System ◽  
Discrete Systems ◽  
Point Theory ◽  
Second Order ◽  
Higher Dimensional ◽  
Image Position

Consider the second-order discrete system where f ∈ C (R × Rm, Rm), f(t + M, Z) = f(t, Z) for any (t, Z) ∈ R × Rm and M is a positive integer. By making use of critical-point theory, the existence of M-periodic solutions of (*) is obtained.

The existence of triangles, tetrahedra, and higher-dimensional simplices with prescribed exradii

2018 ◽  
Vol 102 (554) ◽  
pp. 257-263
Author(s):  
Mowaffaq Hajja
Keyword(s):  
Higher Dimensional ◽  
Image Position

This Article is inspired by a problem that appeared recently in the American Mathematical Monthly, namely 11972 in [1, p. 369]. The problem asks the readers to prove that if r is the inradius of a tetrahedron, and if r1, r2, r3, r4 are its exradii, thenBy taking r = r1 = r2 = r3 = r4 = 1, one sees that (1) is not true for all positive numbers r, r1, r2, r3, r4. This is not surprising, since r is dependent on r1, r2, r3, r4 by the elegant relationwhich we shall prove in Theorem 2 below; see also, for example, [2, (5), §266, p. 92], [3. §41, 2°, (1), p. 76] and [4, Problem 6′(i), p. 39]. Using this relation, one can rewrite (1) asIntuitively, the four numbers r1, r2, r3, r4 are independent, and one may thus ask whether the inequality (3) holds for all positive numbers r1, r2, r3, r4 regardless of being the exradii of some tetrahedron or not.

Asymptotic Expansion of a Class of Multi-Dimensional Integrals

1996 ◽  
Vol 48 (5) ◽  
pp. 1079-1090 ◽  
Author(s):  
A. Sellier
Keyword(s):  
Asymptotic Expansion ◽  
Bounded Function ◽  
Finite Part ◽  
Large Parameter ◽  
One Dimensional ◽  
Higher Dimensional ◽  
The One ◽  
Image Position

AbstractThe aim of this paper is to derive the expansion of the following class of multi-dimensional integralswith respect to the large parameter λ when Ω is a subset of ℝn, a > 0, w is a strictly positive and bounded function on Σ and fp means an integration in the finite part sense of Hadamard (see Section 2). This is performed for weak assumptions bearing on pseudofunction K and by extending to higher dimensional cases the tools developed in the one-dimensional context. The range of applications of the proposed results is outlined by the exhibition of several examples.

scholarly journals On a relation between the topology and the intrinsic and extrinsic geometries of a compact submanifold

1985 ◽  
Vol 28 (3) ◽  
pp. 305-311 ◽  
Author(s):  
Pui-Fai Leung
Keyword(s):  
Compact Riemannian Manifold ◽  
Second Fundamental Form ◽  
Dimensional Euclidean Space ◽  
Gauss Equation ◽  
Intrinsic Geometry ◽  
The Second Fundamental Form ◽  
Higher Dimensional ◽  
Extrinsic Geometry ◽  
Compact Submanifold ◽  
Image Position

Let Mn be an n-dimensional smooth compact Riemannian manifold. By a theorem of Nash, we can think of it as an isometrically immersed submanifold in some higher dimensional Euclidean space ℝn+m. Viewing in this way we can compare the intrinsic geometry of M to its extrinsic geometry. Classically, the Gauss equationwhere K(X,Y) denotes the sectional curvature in M corresponding to the plane spanned by the two orthonormal vectors X, Y and B denotes the second fundamental form gives one of the most important relations between the intrinsic and extrinsic geometries of M. In this note we shall prove the following.

Physical nearest-neighbour models and non-linear time-series: III Non-zero means and sub-critical temperatures

1974 ◽  
Vol 11 (04) ◽  
pp. 715-725 ◽  
Author(s):  
M. S. Bartlett
Keyword(s):  
Linear Time ◽  
Three Dimensional ◽  
Spherical Model ◽  
Nearest Neighbour ◽  
Moment Equations ◽  
Critical Temperatures ◽  
Probability Structure ◽  
Higher Dimensional ◽  
Intrinsic Correlation ◽  
Image Position

The product moment equations previously derived are first discussed for the infinite one- and two-dimensional Ising (or autologistic) model in the case of non-zero mean, as a prelude to an examination of the probability structure in the higher-dimensional (and nominally zero mean) case below the ‘critical temperature’. Of two simple possible models, A and B, both consistent with the division of the product moment p into ergodic, and long-range non-ergodic, components, such that ρ = r (1 – m 2) + m 2, where r is the intrinsic correlation coefficient, it is shown that the second model B appears appropriate to the three-dimensional ‘spherical model’, but the first model A to the Ising model. Model A is defined by xi = yi + M, where M = +m or –m, and E{yi } = 0; and Model B by

An n-dimensional chemotaxis system with signal-dependent motility and generalized logistic source: global existence and asymptotic stabilization

2020 ◽  
pp. 1-21 ◽  
Author(s):  
Wenbin Lv ◽  
Qingyuan Wang
Keyword(s):  
Initial Data ◽  
Global Existence ◽  
Boundary Conditions ◽  
Classical Solution ◽  
Neumann Boundary ◽  
Logistic Source ◽  
Global Classical Solution ◽  
Higher Dimensional ◽  
Image Position ◽  
Chemotaxis System

Abstract This paper deals with the global existence for a class of Keller–Segel model with signal-dependent motility and general logistic term under homogeneous Neumann boundary conditions in a higher-dimensional smoothly bounded domain, which can be written as $$\eqalign{& u_t = \Delta (\gamma (v)u) + \rho u-\mu u^l,\quad x\in \Omega ,\;t > 0, \cr & v_t = \Delta v-v + u,\quad x\in \Omega ,\;t > 0.} $$ It is shown that whenever ρ ∈ ℝ, μ > 0 and $$l > \max \left\{ {\displaystyle{{n + 2} \over 2},2} \right\},$$ then the considered system possesses a global classical solution for all sufficiently smooth initial data. Furthermore, the solution converges to the equilibrium $$\left( {{\left( {\displaystyle{{\rho _ + } \over \mu }} \right)}^{1/(l-1)},{\left( {\displaystyle{{\rho _ + } \over \mu }} \right)}^{1/(l-1)}} \right)$$ as t → ∞ under some extra hypotheses, where ρ+ = max{ρ, 0}.

scholarly journals d-Auslander–Reiten sequences in subcategories

2020 ◽  
Vol 63 (2) ◽  
pp. 342-373
Author(s):  
Francesca Fedele
Keyword(s):  
Abelian Category ◽  
Dimensional Algebra ◽  
Finite Dimensional ◽  
Higher Dimensional ◽  
Image Position ◽  
Cluster Tilting ◽  
Cluster Tilting Subcategory ◽  
Exact Sequences ◽  
Algebra Over A Field

AbstractLet Φ be a finite-dimensional algebra over a field k. Kleiner described the Auslander–Reiten sequences in a precovering extension closed subcategory ${\rm {\cal X}}\subseteq {\rm mod }\,\Phi $. If $X\in \mathcal {X}$ is an indecomposable such that ${\rm Ext}_\Phi ^1 (X,{\rm {\cal X}})\ne 0$ and $\zeta X$ is the unique indecomposable direct summand of the $\mathcal {X}$-cover $g:Y\to D\,{\rm Tr}\,X$ such that ${\rm Ext}_\Phi ^1 (X,\zeta X)\ne 0$, then there is an Auslander–Reiten sequence in $\mathcal {X}$ of the form $${\rm \epsilon }:0\to \zeta X\to {X}^{\prime}\to X\to 0.$$Moreover, when ${\rm En}{\rm d}_\Phi (X)$ modulo the morphisms factoring through a projective is a division ring, Kleiner proved that each non-split short exact sequence of the form $$\delta :0\to Y\to {Y}^{\prime}\buildrel \eta \over \longrightarrow X\to 0$$is such that η is right almost split in $\mathcal {X}$, and the pushout of δ along g gives an Auslander–Reiten sequence in ${\rm mod}\,\Phi $ ending at X.In this paper, we give higher-dimensional generalizations of this. Let $d\geq 1$ be an integer. A d-cluster tilting subcategory ${\rm {\cal F}}\subseteq {\rm mod}\,\Phi $ plays the role of a higher ${\rm mod}\,\Phi $. Such an $\mathcal {F}$ is a d-abelian category, where kernels and cokernels are replaced by complexes of d objects and short exact sequences by complexes of d + 2 objects. We give higher versions of the above results for an additive ‘d-extension closed’ subcategory $\mathcal {X}$ of $\mathcal {F}$.

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