In this paper, we introduce the notion of multiplier in BL-algebra and study relationships between multipliers and some special mappings, likeness closure operators, homomorphisms and (ʘ, Ú)-derivations in BL-algebras. We introduce the concept of idempotent multipliers in BL-algebra and weak congruence and obtain an interconnection between idempotent multipliers and weak congruences. Also, we introduce the special multiplier ap and study some properties. Finally, we show that if A is a boolean algebra, then the set of all multipliers of A is a BL-algebra under some conditions.

We study three kinds of compactness in some variants of Godel logic: compactness, entailment compactness, and approximate entailment compactness.For countable first-order underlying language we use the Henkin construction to prove the compactness property of extensions of first-order Godel logic enriched by nullary connective or the Baaz's projection connective.In the case of uncountable first-order language we use the ultraproduct method to derive the compactness theorem.

Einstein’s theory of relativity made many difficulties for Newtonian physics, so as it did not remain any way for keepingit but setting apart or reforming some of the most fundamental concepts such as space and time. Many thinkers believe that relativity theory made some irreparable hurts on Kant’s philosophy. However, some other thinkers, like Godel, have tried to read relativity theory in such a way that not only have no contradiction with Kant’s philosophy, but also introduce some affirmations for it. This paper casts light on Godel’s effort for reconciling relativity theory with Kant’s philosophy in the topic of ' Time'; It also contains some remarks on the point that how conception of time in relativity theory can lead us to defend Idealism. Finally, it would be suggested that for reconciling Kant’s philosophy with modern science, we should both cease his inflexibility about the process of acquiring knowledge and set apart the hypothesis of being unknowable of the thing-in-itself.

It is known that even duals of a Banach algebra A with one of Arens products are Banach algebras, these products are natu-ral multiplications extending the one on A. But the essence of A ∗,is completely di, erent. By de, ning new products, we investigate some algebraic and spectral properties of odd duals of A. We will show re-lations between these products and Arens products, weak or weak-star continuity, commutativity and unit elements of these algebras. We also determine the spectrum and multiplier algebra for A ∗, , and we calculate the quasi-inverses, spectrum and spectral radius for elements of these kinds of algebras.

For a locally compact group G, let A(G) be the Fourier algebra and let A_M (G) be the completion of this algebra in its multiplier algebra. In this paper, we show that A(G) is an abstract Segal algebra in A_M (G). Also, a necessary and sufficient condition for equality of these two algebras is given. Then we prove that A_M (G) is an ideal in its second dual if and only if G is discrete. We show that if G is a discrete group, then A_M (G) is a BSE algebra if and only if G is M-weakly amenable. As a corollary, it is proven that A_M (F_2 ) is a BSE algebra while A(F_2 ) is not. Finally, we examine our results for the Lebasque-Fourier algebra and also give a completely new proof for equality of the character space of A(G) and A_M (G).

We show that the radical bundle of an algebra bundle is a characteristic ideal bundle. Further we prove an algebra bundle is semisimple if and only if its derivation algebra bundle is either semisimple or zero.

Sound, with all its manifestations, presents itself as a form of energy with properties and capabilities that remain partially shrouded in mystery. The art of composing music, the artful assemblage and fusion of sounds, still lingers in a realm of obscurity, fraught with complexities. The techniques wielded by composers often stem from an intrinsic gift that defies replication or sharing. However, akin to other art forms, music can be deciphered through the lenses of mathematics and geometry. Through the utilization of linear algebra, a paramount mathematical discipline, a practical and efficient framework can be established for the comprehension and manipulation of musical compositions. Within this discourse, we delve into the essence of music and its fundamental principles, subsequently exploring the application of mathematical concepts; linear algebra in particular; in the analysis of music. The findings put forth in this manuscript hold the potential to enlighten researchers and enthusiasts within the realm of music and mathematical sciences, enhance comprehension and knowledge, refine and enhance analytical methodologies and musical procedures across various facets of the music industry, and foster a deeper bond between the realms of mathematics and artistic expression.