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1-Amino-2-(4-pyridyl)-1,3,4-triazole-5-thiol (1) was prepared and transformed into triazolothiadiazenone 2a-b,thiadiazole 3,4a-b,5,6a-b,thiadiazine derivatives 7a-b,8 and also thiourea derivatives 9a-b which converted into thiazin...
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1-Amino-2-(4-pyridyl)-1,3,4-triazole-5-thiol (1) was prepared and transformed into triazolothiadiazenone 2a-b,thiadiazole 3,4a-b,5,6a-b,thiadiazine derivatives 7a-b,8 and also thiourea derivatives 9a-b which converted into thiazine 10 and pyrimidine derivatives 11.The synthesis of triazolethiamine 12,thiatrizine 13,thiadiazole 14,benzothiadiazine 15 and quinoxaline derivatives 16 was also described.
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We develop some aspects of the theory of derivators, pointed derivators and stable derivators. Stable derivators are shown to canonically take values in triangulated categories. Similarly, the functors belonging to a stable deriva...
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We develop some aspects of the theory of derivators, pointed derivators and stable derivators. Stable derivators are shown to canonically take values in triangulated categories. Similarly, the functors belonging to a stable derivator are canonically xact so that stable derivators are an enhancement of triangulated categories. We also establish a similar result for additive derivators in the context of pretriangulated categories. Along the way, we simplify the notion of a pointed derivator, reformulate the base change axiom and give a new proof that a combinatorial model category has an underlying derivator.
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Let L be a Lie algebra, and Der(L) and IDer(L) be the set of all derivations and inner derivations of L, respectively. Also, let Der_c(L) denote the set of all derivations α ∈ Der(L) for which α(x) ∈ Imad_x for all x ∈ L. We ...
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Let L be a Lie algebra, and Der(L) and IDer(L) be the set of all derivations and inner derivations of L, respectively. Also, let Der_c(L) denote the set of all derivations α ∈ Der(L) for which α(x) ∈ Imad_x for all x ∈ L. We give necessary and sufficient conditions under which Der_c(L) = Der_z(L), where Der_z(L) is the set of all derivations of L whose images lie in the center of L. Moreover, it is shown that any two isoclinic Lie algebras L_1 and L_2 satisfy Der_c(L_1) ≌ Der_c(L_2).
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2-Aminopyridine was fused with ethyl acetoacetate without solvent for two hours to yield the N-2-pyridyl-3-oxobutanamide 1. However, when the reaction time was increased to 5 hours a structure 3 was obtained. Condensation of the s...
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2-Aminopyridine was fused with ethyl acetoacetate without solvent for two hours to yield the N-2-pyridyl-3-oxobutanamide 1. However, when the reaction time was increased to 5 hours a structure 3 was obtained. Condensation of the structure 3 with benzaldehyde gave 4. The reaction of pyridopyridone 3 with arylidenemalononitrile 7a-c afforded 4H-pyran derivative 10a-c. In contrast to the behavior of arylidenemalononitrile 7a-c towards pyridopyridine 3, benzylidenemalononitrile 7d reacted with compound 3 to give a product 11. Compound 1 was allowed to react with arylidenemalononitrile to give the dihydropyridine derivative 17a-d. Alkylation of compound 1 with alkylating agents has been also reported. Thus, compound 1 was condensed with [DMF-DMA] in refluxing dioxane to yield 18, but under the reaction conditions we obtained only 21. The pyridopyridone 3 reacted with benzoylisothiocyanate 25a,b to give thiourea derivatives 26a,b Cyclization of 26a,b in dry dioxane and cone, sulphuric acid afforded pyridopyrimidinethione derivatives 27a,b. On the other hand, coupling of pyridopyridine 3 with the aromatic diazonium salt 28a-e afforded the corresponding azo products 29a-e. Boiling of compound 29 in aqueous solution of HCI afforded the hydrazo products 30. Treatment of arylhydrazone 30a with malononitrile afforded the pyridazine derivatives 31,
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Let R be a ring containing a nontrivial idempotent with center Z(R) and N be the set of all non-negative integers. A family D = {d(n)}(n is an element of N) of maps d(n) : R -> R (need not be additive) is said to be a Lie triple h...
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Let R be a ring containing a nontrivial idempotent with center Z(R) and N be the set of all non-negative integers. A family D = {d(n)}(n is an element of N) of maps d(n) : R -> R (need not be additive) is said to be a Lie triple higher derivable if d(n)([[a, b], c]) = Sigma(p+q+r=n) [[d(p)(a), d(q)(b)], d(r)(c)] for all a, b, c is an element of R and for all n is an element of N, where d(0) = I-R (the identity map on R). In the present paper it is shown that if d(n) is a Lie triple higher derivable for each n is an element of N, then there exists an element z(a,b) (depending on a and b) in its center Z(R) such that d(n) (a + b) = d(n)(a) + d(n)(b) + z(a,b), for all n is an element of N.
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Given multivariate time series, we study the problem of forming portfolios with maximum mean reversion while constraining the number of assets in these portfolios. We show that it can be formulated as a sparse canonical correlatio...
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Given multivariate time series, we study the problem of forming portfolios with maximum mean reversion while constraining the number of assets in these portfolios. We show that it can be formulated as a sparse canonical correlation analysis and study various algorithms to solve the corresponding sparse generalized eigenvalue problems. After discussing penalized parameter estimation procedures, we study the sparsity versus predictability trade-off and the significance of predictability in various markets.
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The quantum fractional derivative is defined using formulations analogue to the common Grunwald-Letnikov derivatives. While these use a linear variable scale, the quantum derivative uses an exponential scale and is defined in R~+ ...
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The quantum fractional derivative is defined using formulations analogue to the common Grunwald-Letnikov derivatives. While these use a linear variable scale, the quantum derivative uses an exponential scale and is defined in R~+ or R~-. Two integral formulations similar to the usual Liouville derivatives are deduced with the help of the Mellin transform.
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This paper presents a brief review of derivations used in rings such as orthogonal derivation, orthogonal generalized derivation, orthogonal Jordan derivation, orthogonal symmetric derivation, and orthogonal semiderivation. The st...
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This paper presents a brief review of derivations used in rings such as orthogonal derivation, orthogonal generalized derivation, orthogonal Jordan derivation, orthogonal symmetric derivation, and orthogonal semiderivation. The study of algebraic number theory and ideals had a great impact on the development of ring theory. Julius Wiihelm Richard Dedekind, a famous German mathematician introduced the concepts of fundamentals of ring theory though the name ring has been given later by Hilbert. Dedekind has contributed a lot to abstract algebra, an axiomatic foundation for the natural numbers, algebraic number theory and the definition of the real numbers. In 1879 and 1894 the notions of an ideal had led to the fundamental of ring theory. Algebraic structure plays an important role in ring theory. Some special classes of rings are group ring, division ring, universal enveloping algebra, and polynomial identities. These kinds of rings are used in solving a variety of problems in number theory and algebra. There are many examples of rings found in other areas of mathematics which includes topology and mathematical analysis.
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Purpose - The purpose of this paper is to investigate factors that safeguard or hinder the proper use of derivatives, with evidence from active users and controllers of derivatives. Design/methodology/approach - An online panel of...
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Purpose - The purpose of this paper is to investigate factors that safeguard or hinder the proper use of derivatives, with evidence from active users and controllers of derivatives. Design/methodology/approach - An online panel of 420 users and controllers of derivatives responded to a self-report questionnaire that was purposely designed for the present study. Exploratory factor analysis was used to guide scale construction and the resulting factor scores were examined overall and across four demographic variables (gender, experience, education, position held with firm). Findings - Factor analysis provided support for the five hypothesised dimensions of proper derivative usage: Risk management controls; Misuse; Expertise; Perception; and Benefits. Summary statistics of the factor scores revealed that the respondents agree that: they are giving proper attention to risk management controls; factors such as greed, politics, inappropriate standards and inadequate controls encourage misuse; they are capable of dealing with derivatives even in complex situations; derivatives are valuable financial instruments; and they are aware of the benefits derivatives provide to firms, when properly handled. However, some respondents reported contrasting views while the respondents' education, position held and experience with derivatives produced a significant impact on the factor scores. The implications of the findings are discussed. Originality/value - This study provides a better understanding and assessment of five factors that affect the proper use of derivatives and addresses practical recommendations aimed at ensuring that the true values and qualities of the derivative instrument are not obscured.
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Let X be a Banach space of dimension > 2. We show that every local Lie derivation of B(X) is a Lie derivation, and that a map of B(X) is a 2-local Lie derivation if and only if it has the form \({A \mapsto AT - TA + \psi(A)}\), w...
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Let X be a Banach space of dimension > 2. We show that every local Lie derivation of B(X) is a Lie derivation, and that a map of B(X) is a 2-local Lie derivation if and only if it has the form \({A \mapsto AT - TA + \psi(A)}\), where \({T \in B(X)}\) and ψ is a homogeneous map from B(X) into \({\mathbb{F}I}\) satisfying \({\psi(A + B) = \psi(A)}\) for \({A, B \in B(X)}\) with B being a sum of commutators.
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