We consider a (static) portfolio system that satisfies adding-up constraints and the gross substitution theorem. We show the relationship of the two conditions to the weak dominant diagonal property of the matrix of interest rate elasticities. This enables us to investigate the impact of simultaneous changes in interest rates on the asset demands.

Abstract The constant elasticity of substitution (CES for short) is a basic property widely used in some areas economics that involves system second-order nonlinear partial differential equations. One the most remarkable results mathematical states under homogeneity condition i.e. production function homogeneous certain degree, there are no other models with CES apart from famous Cobb–Douglas a...

In this paper we propose a Weak Lambda Calculus called λPw having explicit operators for Pattern Matching and Substitution. This formalism is able to specify functions defined by cases via pattern matching constructors as done by most modern functional programming languages such as OCAML. We show the main property enjoyed by λPw, namely subject reduction, confluence and strong normalization.

This paper presents a contribution to minimization of intuitionistic fuzzy automata. In this paper the concept of substitution property (SP) partition for a finite intuitionistic fuzzy automaton is formulated, and the quotient automaton with respect to an SP partition is defined.

Anthocyanidins were synthesized to study the effect of methoxy substitution on the B ring to their antioxidant property. Comparative FRAP studies show 2'- and 4'-methoxy substituents have higher antioxidant activities, which may be attributed to both resonance and inductive effects.Graphical abstract:Anthocyanidins as reducing agents.

Using the fact that the class of representable cylindric algebras of infinite dimension fails to have the amalgamation property, we solve an open problem in the monograph “Cylindric Algebras, Part I” by Henkin, Monk and Tarski. Our result applies to other algebras of logic, namely Pinter’s substitution algebras and Halmo’s quasi-polyadic algebras.

The adequacy of substitution matrices to model evolutionary relationships between amino acid sequences can be numerically evaluated by checking the mathematical property of triangle inequality for all triplets of residues. By converting substitution scores into distances, one can verify that a direct path between two amino acids is shorter than a path passing through a third amino acid in the a...

To what measure does the CES (constant elasticity of substitution) property determine production functions? We show that it is not possible to find explicitly all two variable production functions f(x, y) having the CES property. This slightly generalizes the result of R. Sato [16]. We show that if a production function is a quasi-sum then the CES property determines only the functional forms o...

It is well-known that any substitution in intuitionistic propositional logic can be seen as an endomorphism between free Heyting algebras. For a given substitution σ : F (n)→ F (m), (where F (n) is the n-generated free Heyting algebra, n ∈ ω), the theory of σ is the filter σ−1(>). The theory of σ is finitely axiomatizable if σ−1(>) is a principal filter. The formula which generates this filter ...