Let In be the set of partial one-to-one transformations on chain Xn={1,2, . , n} and, for each α in In, let h(α)=|Imα|, f(α)=|{x∈Xn:xα=x}| and w(α)=max(Imα). this note, we obtain formulae involving binomial coefficients F(n; p, m, k)=|{α ∈ In:h(α)=p∧f(α)=m∧w(α)=k}| F(n;·, In:f(α)=m∧w(α)=k}| analogous results derangements In.

The Inverse 3–SAT problem is known to be coNP Complete: Given φ a set of models on n variables, is there a 3–CNF formula such that φ is its exact set of models ? An immediate candidate formula F 3 φ arises, which is the conjunction of all 3–clauses satisfied by all models in φ. The (co)Inverse 3–SAT problem can then be resumed: Given φ a set of models on n variables, is there a model of F 3 φ /...

Diffusion methods were used to investigate the fixation probability, average time until fixation and extinction, and cumulative heterozygosity and genetic variance for single mutant genes in finite populations with partial inbreeding. The critical parameters in the approximation are the coefficient of inbreeding due to nonrandom mating (F) and the effective population size (Ne), which also depe...

In this paper, we prove the boundedness of foliated surfaces $$(X,{{\mathscr {F}}})$$ which are minimal partial du Val resolutions canonical models $$(X_c,{{\mathscr {F}}}_c)$$ general type. For applications, show non-cusp singularities on type and effective generation complement cusp singularities.

In this paper we begin the classification completed in [12] of all partial linear spaces n , graphs F, and groups G which satisfy one of the following: I. II = (0>, ££) is a connected partial linear space of order 2 in which every pair of intersecting lines lies in a subspace isomorphic to the dual of an affine plane of order 2; II. F is a connected graph such that, for each vertex x of F, the ...

1 For f(x, y) = x − 6xy + y, we have fx(x, y) = 4x − 12xy, fxx = 12x − 12y, fy(x, y) = −12xy+4y, fyy = −12x +12y and see that fxx+ fyy = 0. A function which satisfies this equation is also called harmonic. The equation fxx + fyy = 0 is an example of a partial differential equation: it is an equation for an unknown function f(x, y) which involves partial derivatives with respect to more than one...

The papers [15], [16], [4], [12], [2], [14], [5], [1], [3], [7], [6], [10], [11], [8], [9], [17], and [13] provide the notation and terminology for this paper. The following proposition is true (1) For every real number x and for every natural number n holds |x| = |x|. Let f be a partial function from R to R, let Z be a subset of R, and let a be a real number. The functor Maclaurin(f, Z, a) yie...

We construct a total Boolean function f satisfying R(f) = Ω̃(Q(f)), refuting the long-standing conjecture that R(f) = O(Q(f)) for all total Boolean functions. Assuming a conjecture of Aaronson and Ambainis about optimal quantum speedups for partial functions, we improve this to R(f) = Ω̃(Q(f)). Our construction is motivated by the Göös-Pitassi-Watson function but does not use it.

In this study, the traditional full/deficit irrigation and partial root drying (F-PRD) techniques with four different amounts of (100%, 80%, 60% 40%) were examined on Rubygem Strawberry species under controlled greenhouse conditions, in terms yield, yield parameters, WUE, IWUE, response factor (ky), etc. their possible reactions have been investigated. study which fresh seedlings used, planted ...

We present a framework for studying circuit complexity that is inspired by techniques that are used for analyzing the complexity of CSPs. We prove that the circuit complexity of a Boolean function f is characterized by the partial polymorphisms of f ’s truth table. Moreover, the non-deterministic circuit complexity of f is characterized by the polymorphisms of f ’s truth table.