There are many inequalities measuring the deviation of the average of a function over an interval from a linear combination of values of the function and some of its derivatives. A general setting is given from which the desired inequalities are obtained using Hölder’s inequality. Moreover, sharpness of the constants is usually easy to prove by studying the equality cases of Hölder’s inequality. Comparison of averages, extension to weighted integrals and $n$-dimensional results are also given.
The goal of this paper is to examine the conditions of validity for the rule of β-conversion in TIL, which is a hyperintensional, typed λ-calculus of partial functions. The rule of β-reduction is a fundamental computational rule of the λ-calculi and functional programming languages. However, it is a well-known fact that the specification of this rule is ambiguous (see, e.g., Plotkin 1975 or Chang & Felleisen 2012). There are two procedurally non-equivalent ways of executing the rule, namely β-conversion ''by name'' and β-conversion ''by value''. In the λ-calculi conversion by name is usually applied, though it is known that such a conversion is not unconditionally valid when partial functions are involved. If a procedure that is typed to produce an argument value is improper by failing to produce one, conversion by name cannot be validly applied. On the other hand, conversion by value is valid even in the case of improperness. Moreover, we show that in a typed λ-calculus the specification of λ-closure is also not unambiguous. There is an interpretation of this specification under which β-reduction by name is not valid even when the argument procedure does not fail to produce a value. As a result, we present a universally valid rule of β-reduction by value. and Cílem této práce je zkoumat podmínky platnosti pravidla β-konverze v TIL, což je hyperintenzivní, psaný λ-kalkul dílčích funkcí. Pravidlo β-redukce je základním výpočtovým pravidlem λ-kalkulů a funkčních programovacích jazyků. Je však dobře známo, že specifikace tohoto pravidla je nejednoznačná (viz např. Plotkin 1975 nebo Chang & Felleisen 2012). Existují dva procedurálně neekvivalentní způsoby provedení pravidla, a to β-konverze '' podle názvu '' a ''β-konverze'' podle hodnoty'. V kontextu λ-kalkulů se obvykle používá konverze podle názvu, ačkoli je známo, že taková konverze není bezpodmínečně platná, pokud jde o dílčí funkce. Je-li zadaný postup, který má hodnotu parametru argumentu, nesprávný tím, že jej neproběhne, nemůže být konverzace podle názvu platně použita. Na druhé straně konverze hodnotou platí i v případě nevhodnosti. Navíc ukážeme, že v zadaném λ-kalku není specifikace uzavření λ jednoznačná. Existuje interpretace této specifikace, při níž není jméno p-redukce platné, ani když proces argumentu nedokáže vytvořit hodnotu. Výsledkem je obecně platné pravidlo β-redukce hodnotou .
This paper deals with cooperative games with n players and r alternatives which are called multi-alternative games. In the conventional multi-alternative games initiated by Bolger, each player can choose any alternative with equal possibilities. In actual social life, there exist situations in which players have some restrictions on their choice of alternatives. Considering such situations, we study restricted multi-alternative games. A value for a given game is proposed.
The differential evolution (DE) algorithm is a powerful population-based stochastic technique to search for global optimum in the continuous search space. Success of DE algorithm strongly depends on choosing its parameters. The competition in differential evolution was shown to be an efficient instrument to avoid time-consuming process of tuning control parameters. A new variant of competitive DE algorithm, called BEBERAN, was proposed and tested on benchmark functions at four levels of the search space dimension. The BEBERAN was compared with the most promising competitive variant, DEBR18. BEBERAN, in contrast to DEBR18, includes in addition the exponential crossover.
There are two kinds of universal schemes for estimating residual waiting times, those where the error tends to zero almost surely and those where the error tends to zero in some integral norm. Usually these schemes are different because different methods are used to prove their consistency. In this note we will give a single scheme where the average error is eventually small for all time instants, while the error itself tends to zero along a sequence of stopping times of density one.
We address here the problem of scale and rotation invariant object recognition, making use of a correspondence-based mechanism, in which the identity of an object represented by sensory signals is determined by matching it to a representation stored in memory. The sensory representation is in general affected by various transformations, notably scale and rotation, thus giving rise to the fundamental problem of invariant object recognition. We focus here on a neurally plausible mechanism that deals simultaneously with identification of the object and detection of the transformation, both types of information being important for visual processing. Our mechanism is based on macrocolumnar units. These evaluate identity- and transformation-specific feature similarities, performing competitive selection of the alternatives of their own subtask, and cooperate to make a coherent global decision for the identity, scale and rotation of the object.
The Fourier expansion in eigenfunctions of a positive operator is studied with the help of abstract functions of this operator. The rate of convergence is estimated in terms of its eigenvalues, especially for uniform and absolute convergence. Some particular results are obtained for elliptic operators and hyperbolic equations.
We study the stability of a-Browder-type theorems for orthogonal direct sums of operators. We give counterexamples which show that in general the properties (SBaw), (SBab), (SBw) and (SBb) are not preserved under direct sums of operators. However, we prove that if S and T are bounded linear operators acting on Banach spaces and having the property (SBab), then S ⊕ T has the property (SBab) if and only if σSBF− + (S ⊕ T ) = σSBF− + (S) ∪ σSBF− + (T ), where σSBF− + (T ) is the upper semi-B-Weyl spectrum of T . We obtain analogous preservation results for the properties (SBaw), (SBb) and (SBw) with extra assumptions.
In this paper we study the problem of estimation of individual measurements of objects in a biased spring balance weighing design under assumption that the errors are uncorrelated and they have different variances. The lower bound for the variance of each of the estimated measurements for this design and the necessary and sufficient conditions for this lower bound to be attained are given. The incidence matrices of the balanced incomplete block designs are used for construction of the A-optimal biased spring balance weighing design.