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For a Banach algebra $${{\mathcal {A}}}$$ and a norm one character $$\phi $$ on $${{\mathcal {A}}}$$ , we characterize $$\phi $$ -amenability and $$\phi $$ -contractibility of $${{\mathcal {A}}}$$ in terms of metrically homological properties of some Banach $${\mathcal A}$$ -modules. Also, for any Banach $${{\mathcal {A}}}$$ -module, metrically injectivity and projectivity of submodules and quotient modules are investigated. Finally, we give some results on metrically injectivity of $${{\mathcal {A}}}^*$$ and its submodules.

Tourism industry is an integrated system that its elements can be correlated. Providing accommodation constitutes one of the dynamic sectors of tourism. The situation of these centers is considered as the most important factor in their success. The establishment of each urban element in a spatial-physical situation is governed by particular rules, principles, and mechanisms which, if met, they will result in the success and efficiency of that element at the same certain place. In locating the residential centers, we need to have criteria and indicators in order to compare between places, more convenient and locating be more precise. The aim of this study is also to provide criteria for site selection of rural tourism services. This research has been done as analytical and has been carried out as a library one. The results show that some principles and criteria to locate villages having tourism attractions includedensity, residential places and tourism installations and tourism facilities, public facilities, employment, transportation, allowed threshold in environment, comfort threshold and natural thresholds. To distribute the tourism services in a rural area according to the current capacity, limits to acceptable change, zoning, license and permission, environmental standards and designing criteria should be considered. Distribution of tourism services in places having attraction and intervention in existing area necessitate the existence of certain rules and regulations and correspondence with local conditions. Therefore, it is essential to legalize intervention in the fields and physical planning, the specific rules and regulations should be developed in each level of planning.

In this article, some properties such as the approximation property of non-zero nilpotent ideals in generalized amenable Banach algebras are investigated. Also, we show that in pseudo-contractible Banach algebras, non-zero nilpotent ideals cannot have the approximation property.

The slaughterhouse, whether it is seen as an institution, as an industry, or as a unique technological system, is arguably right at the heart of modernism. Human–animal relationships and more generally human–nature relationships bring about issues of rationalization, alienation, and commodity fetishism, while raising philosophical concerns of the human worldview. Current practices of animal slaughter in Iran challenge the core values of Islamic teachings. Slaughterhouses are hidden from the public, segregated into various sections, and follow the exact same models of industrial production as in other parts of the world. Since they must abide by Islamic ways of slaughter and therefore become Halal, these slaughterhouses are slightly modified accordingly. When meat, or what is recently referred to as protein, shows up in the market, it conceals any sign of its true origin—it is neatly packaged with layers of plastic and modern colorful labels showing animals happily grazing on open, green pasture. T...

In this paper, we introduce the notion of derivations for a trellis and investigate some related properties of this subject. We give some equivalent conditions under which a derivation is isotone for trellises. Also, we study fixed points and define f-derivation on T and Cartesian derivation on T1 × T2.

We extend the concept of Arens regularity of a Banach algebra \(\mathcal{A}\) to the case that there is an \(\mathcal{O}\) -module structure on \(\mathcal{A}\) , and show that when S is an inverse semigroup with totally ordered subsemigroup E of idempotents, then A=l1(S) is module Arens regular if and only if an appropriate group homomorphic image of S is finite. When S is a discrete group, this is just Young’s theorem which asserts that l1(S) is Arens regular if and only if S is finite.