A MIXED MULTIFRACTAL ANALYSIS FOR QUASI-AHLFORS VECTOR-VALUED MEASURES

The multifractal formalism for measures in its original formulation is checked for special classes of measures, such as, doubling, self-similar, and Gibbs-like ones. Out of these classes, suitable conditions should be taken into account to prove the validity of the multifractal formalism. In this work, a large class of measures satisfying a weak condition known as quasi-Ahlfors is considered in the framework of mixed multifractal analysis. A joint multifractal analysis of finitely many quasi-Ahlfors probability measures is developed. Mixed variants of multifractal generalizations of Hausdorff, and packing measures, and corresponding dimensions are introduced. By applying convexity arguments, some properties of these measures, and dimensions are established. Finally, an associated multifractal formalism is introduced, and proved to hold for the class of quasi-Ahlfors measures. Besides, some eventual applications, and motivations, especially, in AI are discussed.

On semilocal convergence of three-step Kurchatov method under weak condition

The purpose of this paper to establish the semilocal convergence analysis of three-step Kurchatov method under weaker conditions in Banach spaces. We construct the recurrence relations under the assumption that involved first-order divided difference operators satisfy the $$\omega $$ ω condition. Theorems are given for the existence-uniqueness balls enclosing the unique solution. The application of the iterative method is shown by solving nonlinear system of equations and nonlinear Hammerstein-type integral equations. It illustrates the theoretical development of this study.

1917

This chapter focuses on the deaths of the people who died in Ireland in 1917. Some of these deaths were those of the released 1916 Rising prisoners, including packaging porter Christopher Brady, who was released due to ill-health and died at home from pneumonia. Other 1916 Rising prisoners, like carpenter Bernard Ward, died from prison-related illness. Trade unionist engineer William Partridge, who died two months after release from Lewes on medical grounds and whose 'death was due to prison treatment', became a union official after losing his railway job for protesting at the preferential promotion of Protestants. Meanwhile, schoolteacher Thomas Ashe was jailed in Mountjoy for a seditious speech, during which he and others went on hunger strike for political status. Ashe died due to 'heart failure and congestion of the lungs caused by being left to lie on the cold floor for fifty hours and then subjected to forcible feeding in his weak condition after hunger strike'. Police reported that Ashe's death 'evoked demonstrations of sympathy on the part of Nationalists' across Ireland and gave a fresh impetus to the Sinn Féin movement.

PENGARUH NILAI TUKAR TERHADAP HARGA SAHAM PERUSAHAAN SEKTOR FOOD AND BEVERAGE DI MASA PANDEMI COVID-19

The purpose of this study is to examine the effect of exchange rates on stock prices during the Covid-19 pandemic era. The population in this study was food and beverage companies listed on the Indonesia Stock Exchange. The research period was four months, from January 2, 2020, to May 8, 2020. Research data were collected based on the weak condition of the world economy and the Indonesian economy as the impact of Covid-19 and based on the phenomenon that the food and beverage business will reap profits amid the pandemic. This study used linear regression analysis with e-Views software. The results showed that the exchange rate affects the stock price of companies engaged in the food and beverage sector listed on the Indonesia Stock Exchange. Keywords: exchange rate, food and beverage, stock price

Short report on probable case of Caspian Gull predation on migrating swallows observed at first time

At Mietków Reservoir (SW Poland), during the breeding season of 2019, we found 52 dead swallows in Caspian Gull (Larus cachinnans) colony. Most of them were Barn Swallows (Hirundo rustica). The bodies of swallows were fresh and torn with traces of bill. We assume that swallows might have been in weak condition and hunted by gulls. They also could die because of bad weather conditions and hypothermia, fell into the water and then were taken. However, to our knowledge, it was the first mass event of feeding on migrating birds by Caspian Gull.

Wilkinson’s Bus: Weak Condition Numbers, with an Application to Singular Polynomial Eigenproblems

We propose a new approach to the theory of conditioning for numerical analysis problems for which both classical and stochastic perturbation theories fail to predict the observed accuracy of computed solutions. To motivate our ideas, we present examples of problems that are discontinuous at a given input and even have infinite stochastic condition number, but where the solution is still computed to machine precision without relying on structured algorithms. Stimulated by the failure of classical and stochastic perturbation theory in capturing such phenomena, we define and analyse a weak worst-case and a weak stochastic condition number. This new theory is a more powerful predictor of the accuracy of computations than existing tools, especially when the worst-case and the expected sensitivity of a problem to perturbations of the input is not finite. We apply our analysis to the computation of simple eigenvalues of matrix polynomials, including the more difficult case of singular matrix polynomials. In addition, we show how the weak condition numbers can be estimated in practice.

Asymptotic escape rates and limiting distributions for multimodal maps

We consider multimodal maps with holes and study the evolution of the open systems with respect to equilibrium states for both geometric and Hölder potentials. For small holes, we show that a large class of initial distributions share the same escape rate and converge to a unique absolutely continuous conditionally invariant measure; we also prove a variational principle connecting the escape rate to the pressure on the survivor set, with no conditions on the placement of the hole. Finally, introducing a weak condition on the centre of the hole, we prove scaling limits for the escape rate for holes centred at both periodic and non-periodic points, as the diameter of the hole goes to zero.