Tensile behavior of a Brazilian Disk Containing non-persistent Joint Sets Subjected to Diametral Loading: An Experimental Investigation

Structural defects are part of the inherent characteristics of rock masses. They can be found in the form of fishers, joints, and beddings and can be divided into persistent or non-persistent one. The coalescence of non-persistent cracks may lead to the formation of persistent joints under the tensile stress field, leading to instability of rock mass. The mechanical behavior of non-persistent jointed disks under tensile stress has essential implications for rock engineering structures. In this paper, concrete Brazilian disks containing open non-persistent joints were constructed and subjected to diametral loading to investigate the effect of this kind of joint parameters on the tensile strength and stiffness of disks. The effect of some parameters, such as joint continuity factor (the relationship between joint length and rock bridge length), bridge angle, joint spacing, and loading direction with respect to joint angle were investigated to estimate the tensile strength and stiffness as well as failure pattern. The results of experiments revealed that the tensile strength, stiffness, and failure pattern of Brazilian disks are highly affected by non-persistent pre-existing crack parameters. The increase of joint continuity factor and loading direction leads to an increase in tensile strength and a decrease in stiffness. However, when bridge angle and spacing increase tensile strength rises, and the former decreases stiffness while the latter results in its reduction. Finally, all the parameters significantly affect the failure pattern, and some failure patterns such as step-path failure, splitting, or sliding may occur as a function of non-persistent joint parameters.

On the joint continuity of topological pressures for sub-additive singular-valued potentials

Given a non-conformal repeller [Formula: see text] of a [Formula: see text] map [Formula: see text], we give a variational principle of a dimensional upper bound of the non-conformal repellers. If [Formula: see text] is [Formula: see text] then we prove the joint continuity of topological pressure for sub-additive singular-valued potentials on maps and parameters.

Points of Continuity of Quasi-Continuous Functions

We study points of joint continuity of multi-variable separately quasi-continuous functions which are continuous with respect to one variable. We will show that the assumption of complete regularity in the paper of V. Maslyuchenko et al in ”Tatra Mt. Math. Pub. 68, (2017), 47–58” can be removed in some situations. Moreover, we use a topological game argument to prove that the set of points of continuity of functions with closed graph into ωΔ-spaces is a Gδ subset of its domain provided that its domain is a W-space.

ON A PROBLEM OF TALAGRAND CONCERNING SEPARATELY CONTINUOUS FUNCTIONS

We construct a separately continuous function $e:E\times K\rightarrow \{0,1\}$ on the product of a Baire space $E$ and a compact space $K$ such that no restriction of $e$ to any non-meagre Borel set in $E\times K$ is continuous. The function $e$ has no points of joint continuity, and, hence, it provides a negative solution of Talagrand’s problem in Talagrand [Espaces de Baire et espaces de Namioka, Math. Ann.270 (1985), 159–164].

CONTINUITY OF A CONDITION SPECTRUM AND ITS LEVEL SETS

Let ${\mathcal{A}}$ be a complex unital Banach algebra, let $a$ be an element in it and let $0<\unicode[STIX]{x1D716}<1$. In this article, we study the upper and lower hemicontinuity and joint continuity of the condition spectrum and its level set maps in appropriate settings. We emphasize that the empty interior of the $\unicode[STIX]{x1D716}$-level set of a condition spectrum at a given $(\unicode[STIX]{x1D716},a)$ plays a pivotal role in the continuity of the required maps at that point. Further, uniform continuity of the condition spectrum map is obtained in the domain of normal matrices.

Joint Continuity of Separately Continuous Mappings with Values in Completely Regular Spaces

We prove general theorems on quasi-continuity of mappings f : X1 × ⋯ × Xn → Z with values in a completely regular space Z. As consequences, we obtain results on joint continuity of separately continuous functions of several variables involving the previous results of several authors.

Equi-Cliquishness and The Hahn Property

We study the joint continuity of mappings of two variables. In particular, we show that for a Baire space X, a second countable space Y and a metric space Z, a map f : X × Y → Z has the Hahn property (i.e., there is a residual subset A of X such that A × Y ⊆ C(f)) if and only if f is locally equi-cliquish with respect to y and {x ∈ X: fx is continuous} is a residual subset of X.