In this paper, we study the binary relations R on a nonempty N-set A which are hindependent and h-positive (cf. the introduction below). They are called homothetic positive orders. Denote by B the set of intervals of R having the form [r,+∞[ with 0 < r ≤ +∞ or ]q,∞[ with q ∈ Q≥0. It is a Q>0-set endowed with a binary relation > extending the usual one on R>0 (identified with a subset of B via t...

In this paper, we revisit the classical mechanism to produce [Formula: see text]-dimensional spacetimes via Kaluza–Klein compactification. We made assumption that bulk geometry text] admits a Homothetic Vector Field (HVF) relaxing existence of zero i.e. holds on and homothetic bivector text]. Under these circumstances, identify origin positive cosmological constant in spacetime as factor repres...

In an incomplete market, with incompleteness stemming from stochastic factors imperfectly correlated with the underlying stocks, we derive representations of homothetic (power, exponential and logarithmic) forward performance processes in factor-form using ergodic BSDE. We also develop a connection between the forward processes and infinite horizon BSDE, and, moreover, with risk-sensitive optim...

We give a characterization of the non-empty binary relations  on a N∗-set A such that there exist two morphisms of N∗-sets u1, u2 : A → R+ verifying u1 ≤ u2 and x  y ⇔ u1(x) > u2(y). They are called homothetic interval orders. If  is a homothetic interval order, we also give a representation of  in terms of one morphism of N∗-sets u : A → R+ and a map σ : u(R+) × A → R+ such that x  y ⇔ σ(...

It should now become obvious the our profit and cost functions derived from production functions, and demand functions derived from utility functions are all homogeneous functions. Using these functions offers us ease of interpretation of key economic ideas. Consider the following idea related to production functions, the returns to scale. Let f(x) be the production function. Then if it were ho...

We study a class of symmetric, quasi-homothetic preferences that result in demands logarithmic in own prices when these have a negligible impact on aggregate price indices (as in monopolistic competition models). Thus marginal revenues are computationally friendly, and decreasing whenever demands are elastic. Preferences can be represented either by an additive negative exponential direct utili...

The counterpart for Euler’s buckling problem is Greenhill’s problem, which studies the forming of a loop in an elastic beam under torsion. In context twisted shafts, optimal shape along its axis searched. A priori form cross-section remains unknown. For solution actual stability equations take into account all possible convex and simply connected shapes cross-section. cross-sections are similar...