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In this paper, we present two type of contributions to the study of two-phases problems. In such problems, the main focus is on optimising a diffusion function α under L∞ and L¹ constraints, this function a appearing in a diffusive term of the form -∇ · (a∇) in the model, in order to maximise a certain criterion. We provide a parabolic Talenti inequality and a partial bang-bang property in radial geometries for a general class of elliptic optimisation problems: namely, if a radial solution exists, then it must saturate, at almost every point, the L∞ constraints defining the admissible class. This is done using an oscillatory method. [ABSTRACT FROM AUTHOR]

In the present paper, we study a multiscale limit for the barotropic Navier-Stokes system with Coriolis and gravitational forces, for vanishing values of the Mach, Rossby and Froude numbers (Ma, Ro and Fr, respectively). The focus here is on the effects of gravity: albeit remaining in a low stratification regime Ma/Fr → 0, we consider scaling for the Froude number which go beyond the "critical" value Fr = √Ma. The rigorous derivation of suitable limiting systems for the various choices of the scaling is shown by means of a compensated compactness argument. Exploiting the precise structure of the gravitational force is the key to get the convergence. [ABSTRACT FROM AUTHOR]

We give a counterexample in this amendment to show that there is an error in consideration of the statement "if f: X → Y and J is an ideal on Y, then f-1(J) = ff-1(J): J ℇ J- is an ideal on X" by Hamlett in his paper "Lindelöf with respect to an ideal" [New Zealand J. Math. 42, 115-120, 2012]. We also modify it here in a new way and henceforth put forward correctly all the results that were based on the said statement derived therein. [ABSTRACT FROM AUTHOR]

Copyright of Proceedings of the Estonian Academy of Sciences is the property of Teaduste Akadeemia Kirjastus and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Proceedings of the Estonian Academy of Sciences is the property of Teaduste Akadeemia Kirjastus and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The main aim of this paper is to present a technical result, which provides an algorithm to prove several cardinal inequalities and relative versions of cardinal inequalities related. Moreover, we use this result and the weak Hausdorff number, H*, introduced by Bonanzinga in [Houston J. Math. 39 (3) (2013), 1013-1030], to generalize some upper bounds on the cardinality of topological spaces. [ABSTRACT FROM AUTHOR]

In this paper, we prove the following statements: (1) There exists a pseudocompact star σ-compact Tychonoff space having a regular-closed subspace which is not star σ-compact. (2) Assuming 2N0 = 2N1 , there exists a star countable (hence star σ-compact) normal space having a regular-closed subspace which is not star σ-compact. [ABSTRACT FROM AUTHOR]

Abstract: A space is said to be -homogeneous provided there are exactly two orbits for the action of the group of homeomorphisms of the space onto itself. Certain conditions on a compactum X are known under which the cone over X is -homogeneous (Nadler Jr. and Pellicer-Covarrubias (2007) ). In this paper we investigate -homogeneity in suspensions of compact metric spaces; namely, we determine necessary and sufficient conditions under which the suspension of a continuum X is -homogeneous, among certain classes of continua. This paper gives a partial answer to a question posed by S.B. Nadler Jr. (2007) in . [Copyright &y& Elsevier]

In this paper we obtain some Cheeger-Gromov-Taylor type compactness theorems for a forward complete and connected Finsler manifold of dimensional n ≥ 2 via weighted Ricci curvatures. The proofs are based on the index form of a minimal unit speed geodesic segment, Bochner-Weitzenböck formula and Hessian comparison theorem. [ABSTRACT FROM AUTHOR]

The multiplication of a semitopological (quasitopological) group G is called sequentially continuous if the product map of G × G into G is sequentially continuous. In this paper, we mainly consider the properties of semitopological (quasitopological) groups with sequentially continuous multiplications and three-space problems in quasitopological groups. It is showed that (1) every snf -countable semitopological group G with the sequentially continuous multiplication is sof -countable; (2) if G is a sequential quasitopological group with the sequentially continuous multiplication, then G contains a closed copy of S ω if and only if it contains a closed copy of S 2 , which give a partial answer to a problem posed by R.-X. Shen; (3) let G be a quasitopological group with the sequentially continuous multiplication, then the following are equivalent: (i) G is a sequential α 4 -space; (ii) G is Fréchet; (iii) G is strongly Fréchet; (4) (MA+¬CH) there exists a non-metrizable, separable, normal and Moore quasitopological group; (5) some examples are constructed to show that metrizability, first-countability and second-countability are not three-space properties in the class of quasitopological groups. [ABSTRACT FROM AUTHOR]

Our aim is to study the total variation flow in metric graphs. First, we define the functions of bounded variation in metric graphs and their total variation, we also give an integration by parts formula. We prove existence and uniqueness of solutions and that the solutions reach the mean of the initial data in finite time. Moreover, we obtain explicit solutions. [ABSTRACT FROM AUTHOR]

This paper addresses the properties of the C 0 -semigroup generated by the reparable system with finite repair time. In particular, it can be shown that the C 0 -semigroup is eventually differentiable and eventually compact, which is not true for the case when the repair time is infinite, as discussed in [9] and [11] . [ABSTRACT FROM AUTHOR]

Two dichotomy theorems on the effective σ-boundedness and effective σ-compactness of ordinal definable point sets in Solovay's model are proved. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we find a necessary and sufficient condition for an -compact space to be -compact. [Copyright &y& Elsevier]

Abstract: In this paper, we classify topologically the homeomorphism groups of infinite graphs Γ with respect to the compact-open and the Whitney topologies. [Copyright &y& Elsevier]

In this paper, we introduce and discuss minimal γ-open sets in topological spaces. We establish some basic properties of minimal γ-open sets and provide an example to illustrate that minimal γ-open sets are independent of minimal open sets introduced and discussed in [3]. We obtain some properties of pre γ-open sets using properties of minimal γ-open sets. As an application of a theory of minimal γ-open sets, we obtain a sufficient condition for a γ-locally finite space to be a pre γ-T2 space. [ABSTRACT FROM AUTHOR]

In this paper, we produce an elementary approach to Thurston''s theory of measured laminations on compact surfaces with non-empty boundary. We show that the theory can be derived from a simple inequality for geometric intersection numbers between arcs inside an octagon. [Copyright &y& Elsevier]

In this article, we study the following bi-nonlocal Kirchhoff-Schr o ¨ dinger-Poisson system with critical growth: { − (∫ Ω | ∇ u | 2 d x) r Δ u + ϕ u = u 5 + λ (∫ Ω F (x , u) d x) s f (x , u) , i n Ω , − Δ ϕ = u 2 , u > 0 , i n Ω , u = ϕ = 0 , o n ∂ Ω , where Ω ⊂ R 3 is a smooth bounded domain, λ > 0 , 0 ≤ r < 1 , 0 < s < 1 − r 3 (r + 1) and f (x , u) satisfies some suitable assumptions. By using the concentration compactness principle, the multiplicity of positive solutions for the above system is established. [ABSTRACT FROM AUTHOR]

Under Jensen's axiom, a compact space X of uncountable character such that the space exp( X) \ X is normal for each n is constructed. Thereby, it is proved that the Arkhangel'skii-Kombarov theorem on the countability of the character of a compact space whose square is normal outside the diagonal cannot be 'naïvely' carried over to normal functors of finite degree. [ABSTRACT FROM AUTHOR]

In this note we prove compactness for the Cahn–Hilliard functional without assuming coercivity of the multi-well potential. [ABSTRACT FROM AUTHOR]

The concepts of P-compactness, countable P-compactness, the P-Lindelöf property are introduced in L-topological spaces by means of preopen L-sets and their inequalities when L is a complete DeMorgan algebra. These definitions do not rely on the structure of the basis lattice L and no distributivity in L is required. They can also be characterized by means of preclosed L-sets and their inequalities. Their properties are researched. Further when L is a completely distributive DeMorgan algebra, their many characterizations are presented. [ABSTRACT FROM AUTHOR]