scholarly journals Buying Supermajorities in Finite Legislatures

2000 ◽  
Vol 94 (3) ◽  
pp. 677-681 ◽  
Author(s):  
Jeffrey S. Banks
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Necessary Condition ◽  
Vote Buying ◽  
Necessary And Sufficient ◽  
Coalition Size

I analyze the finite-voter version of the Groseclose and Snyder vote-buying model. I identify how the optimal coalition size varies with the underlying preference parameters; derive necessary and sufficient conditions for minimal majority and universal coalitions to form; and show that the necessary condition for minimal majorities found in Groseclose and Snyder is incorrect.

scholarly journals On circulant codes with prescribed distances

1977 ◽  
Vol 16 (3) ◽  
pp. 361-369
Author(s):  
M. Deza ◽  
Peter Eades
Keyword(s):  
Sufficient Conditions ◽  
Difference Sets ◽  
Necessary And Sufficient Conditions ◽  
Necessary Condition ◽  
Weighing Matrices ◽  
Cyclic Difference Sets ◽  
The Matrix ◽  
Circulant Codes ◽  
Necessary And Sufficient ◽  
Square Matrix

Necessary and sufficient conditions are given for a square matrix to te the matrix of distances of a circulant code. These conditions are used to obtain some inequalities for cyclic difference sets, and a necessary condition for the existence of circulant weighing matrices.

scholarly journals Square roots in finite full transformation semigroups

1982 ◽  
Vol 23 (2) ◽  
pp. 137-149 ◽  
Author(s):  
Mary Snowden ◽  
J. M. Howie
Keyword(s):  
Transformation Semigroup ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Necessary Condition ◽  
Square Root ◽  
Transformation Semigroups ◽  
Full Transformation ◽  
Square Roots ◽  
Finite Set ◽  
Necessary And Sufficient

Let X be a finite set and let (X) be the full transformation semigroup on X, i.e. the set of all mappings from X into X, the semigroup operation being composition of mappings. This paper aims to characterize those elements of (X) which have square roots. An easily verifiable necessary condition, that of being quasi-square, is found in Theorem 2, and in Theorems 4 and 5 we find necessary and sufficient conditions for certain special elements of (X). The property of being compatibly amenable is shown in Theorem 7 to be equivalent for all elements of (X) to the possession of a square root.

scholarly journals The necessary and sufficient conditions for wavelet frames in Sobolev space over local fields

2021 ◽  
Vol 39 (3) ◽  
pp. 81-92
Author(s):  
Ashish Pathak ◽  
Dileep Kumar ◽  
Guru P. Singh
Keyword(s):  
Sobolev Space ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Local Fields ◽  
Necessary Condition ◽  
Wavelet Frame ◽  
Wavelet Frames ◽  
Necessary And Sufficient

In this paper we construct wavelet frame on Sobolev space. A necessary condition and sufficient conditions for wavelet frames in Sobolev space are given.

scholarly journals Generalising the Horodecki criterion to nonprojective qubit observables

2021 ◽  
Author(s):  
Michael J W Hall ◽  
Shuming Cheng
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Necessary Condition ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Weak Measurements ◽  
Chsh Inequality ◽  
Bell Nonlocality ◽  
Necessary And Sufficient ◽  
Projective Measurements

Abstract The Horodecki criterion provides a necessary and sufficient condition for a two-qubit state to be able to manifest Bell nonlocality via violation of the Clauser-Horne-Shimony-Holt (CHSH) inequality. It requires, however, the assumption that suitable projective measurements can be made on each qubit, and is not sufficient for scenarios in which noisy or weak measurements are either desirable or unavoidable. By characterising two-valued qubit observables in terms of strength, bias, and directional parameters, we address such scenarios by providing necessary and sufficient conditions for arbitrary qubit measurements having fixed strengths and relative angles for each observer. In particular, we find the achievable maximal values of the CHSH parameter for unbiased measurements on arbitrary states, and, alternatively, for arbitrary measurements on states with maximally-mixed marginals, and determine the optimal angles in some cases. We also show that for certain ranges of measurement strengths it is only possible to violate the CHSH inequality via biased measurements. Finally, we use the CHSH inequality to obtain a simple necessary condition for the compatibility of two qubit observables.

scholarly journals Equality of Dedekind sums mod ℤ, 2ℤ and 4ℤ

2015 ◽  
Vol 11 (06) ◽  
pp. 1735-1738 ◽  
Author(s):  
Emmanuel Tsukerman
Keyword(s):  
Necessary Conditions ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Dedekind Sums ◽  
Necessary Condition ◽  
Necessary And Sufficient ◽  
Condition B

In [K. Girstmair, A criterion for the equality of Dedekind sums mod ℤ, Int. J. Number Theory10 (2014) 565–568], it was shown that the necessary condition b ∣ (a1a2- 1) × (a1- a2) for equality of two Dedekind sums s(a1, b) and s(a2, b) given in [S. Jabuka, S. Robins and X. Wang, When are two Dedekind sums equal? Int. J. Number Theory7 (2011) 2197–2202] is equivalent to 12s(a1, b) - 12s(a2, b) ∈ ℤ. In this paper, we give a new proof of this result and then find two additional necessary and sufficient conditions for 12s(a1, b) - 12s(a2, b) ∈ 2ℤ, 4ℤ. These give new necessary conditions on equality of Dedekind sums.

scholarly journals On the Solutions of Second-Order Differential Equations with Polynomial Coefficients: Theory, Algorithm, Application

Algorithms ◽  
2020 ◽  
Vol 13 (11) ◽  
pp. 286
Author(s):  
Kyle R. Bryenton ◽  
Andrew R. Cameron ◽  
Keegan L. A. Kirk ◽  
Nasser Saad ◽  
Patrick Strongman ◽  
...  
Keyword(s):  
Differential Equations ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Linear Differential Equations ◽  
Theoretical Physics ◽  
Necessary Condition ◽  
Polynomial Solutions ◽  
Polynomial Coefficients ◽  
Linear Differential ◽  
Necessary And Sufficient

The analysis of many physical phenomena is reduced to the study of linear differential equations with polynomial coefficients. The present work establishes the necessary and sufficient conditions for the existence of polynomial solutions to linear differential equations with polynomial coefficients of degree n, n−1, and n−2 respectively. We show that for n≥3 the necessary condition is not enough to ensure the existence of the polynomial solutions. Applying Scheffé’s criteria to this differential equation we have extracted n generic equations that are analytically solvable by two-term recurrence formulas. We give the closed-form solutions of these generic equations in terms of the generalized hypergeometric functions. For arbitrary n, three elementary theorems and one algorithm were developed to construct the polynomial solutions explicitly along with the necessary and sufficient conditions. We demonstrate the validity of the algorithm by constructing the polynomial solutions for the case of n=4. We also demonstrate the simplicity and applicability of our constructive approach through applications to several important equations in theoretical physics such as Heun and Dirac equations.

On finitely Bernoulli one-sided Markov shifts and their cofiltrations

1999 ◽  
Vol 19 (6) ◽  
pp. 1527-1564
Author(s):  
BEN-ZION RUBSHTEIN
Keyword(s):  
Transition Matrix ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Necessary Condition ◽  
Skew Product ◽  
Measurable Partition ◽  
Point Extension ◽  
Markov Shifts ◽  
Necessary And Sufficient ◽  
Stationary Vector

The problem under consideration is: when is a Markov endomorphism (one-sided shift) $T=T_P$ with transition matrix $P$, isomorphic to a Bernoulli endomorphism $\tilde{T}_\rho$ with an appropriate stationary vector $\rho=\{\rho_i\}_{i\in I}$? An obvious necessary condition is that there exists an independent complement $\delta$ of the measurable partition $T^{-1}\varepsilon$ with $\distr \delta = \rho$. In this case the cofiltration (decreasing sequence of measurable partitions) $\xi(T)=\{T^{-n}\varepsilon\}^{\infty}_{n=1}$ generated by $T$ is finitely isomorphic to the standard Bernoulli cofiltration $\xi(\tilde{T}_{\rho})=\{\tilde{T}^{-n}_{\rho}\varepsilon\}^{\infty}_{n=1}$ and $T$ is called finitely $\rho$-Bernoulli.We show that every ergodic Markov endomorphism $T_P$, which is finitely Bernoulli, can be represented as a skew product over $\tilde{T}_{\rho}$ with $d$-point fibres $(d\in \mathbb{N})$. We compute the minimal $d=d(T_P)$ in these skew-product representations by means of the transition matrix, and obtain necessary and sufficient conditions under which $d(T_P)=1$, i.e. $T_P$ is isomorphic to $\tilde{T}_{\rho}$. The cofiltration $\xi(T)$ of any finitely Bernoulli ergodic Markov endomorphism $T=T_P$ is represented as a $d$-point extension of the standard cofiltration $\xi(\tilde{T}_{\rho})$, and we show that the minimal $d=d_{\xi}(T)$ in these extensions is equal to $d(T)$. In particular, $d(T)=1\Longleftrightarrow d_{\xi}(T)=1$, that is, a Markov endomorphism $T$ is isomorphic to $\tilde{T}_{\rho}$ iff $\xi(T)$ is isomorphic to the Bernoulli cofiltration $\xi(\tilde{T}_{\rho})$.

scholarly journals Sur la théorie spectrale locale des shifts à poids opérateurs

2005 ◽  
Vol 2005 (21) ◽  
pp. 3497-3509 ◽  
Author(s):  
Mohamed Houimdi ◽  
Hassane Zguitti
Keyword(s):  
Spectral Properties ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Necessary Condition ◽  
Sufficient Condition ◽  
Unilateral Shift ◽  
Nous Montrons ◽  
Necessary And Sufficient

Nous étudions les propriétés spectrales locales du shift unilateral à poids opérateurs. Nous donnons une condition nécessaire et suffisante pour que l'adjoint satisfasse la propriété de l'extension unique (SVEP). Une condition suffisante pour satisfaire la propriété de Dunford (C) ainsi qu'une condition nécessaire pour satisfaire la condition de Bishop (β) seront données. Enfin, nous montrons que le shift à poids opérateurs est décomposable si, et seulement si, il est quasinilpotent.We study the local spectral properties for the unilateral shift with operator-valued weights. We give necessary and sufficient conditions for the adjoint to satisfy the SVEP. Sufficient condition to satisfy Dunford's property (C) and necessary condition to satisfy Bishop's condition (β) are given. Finally we show that the unilateral shift with operator-valued weights is decomposable if and only if it is quasinilpotent.

Substitution, Complementarity, and Stability

2019 ◽  
Vol 21 (01) ◽  
pp. 1940006
Author(s):  
Harborne W. Stuart
Keyword(s):  
Additional Condition ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
The Other ◽  
Necessary Condition ◽  
Sufficient Condition ◽  
Assignment Games ◽  
The Core ◽  
The Many ◽  
Necessary And Sufficient

We provide necessary and sufficient conditions for a non-empty core in many-to-one assignment games. When players on the “many” side (buyers) are substitutes with respect to any given player on the other side (firms), we show that non-emptiness requires an additional condition that limits the competition among the buyers. When buyers are complements with respect to any given firm, a sufficient condition for non-emptiness is that buyers also be complements with respect to all of the firms, collectively. A necessary condition is that no firm can be guaranteed a profit when the core is non-empty.

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