If f(x1, ..., xn) ∈ Z[x1, ..., xn] has the property that every integer specialization gives an integral square value, then f is itself the square of a polynomial. We also give an effective version of this result by using an effective version of a classical theorem of E. Noether along with a theorem of Lang and Weil.

the option-pricing problem is always an important part in modern finance. assuming that the stock diffusion is a constant, some literature has introduced many stock models and given corresponding option pricing formulas within the framework of the uncertainty theory. in this paper, we propose a new stock model with uncertain stock diffusion for uncertain markets. some option pricing formulas on...

In this article, we have discussed Morris and Thorne (MT) wormhole solutions in a modified theory of gravity that admits conformal motion. Here, explore the [Formula: see text] gravity, which is function Ricci scalar ([Formula: text]) trace stress–energy tensor text]). To study geometries, make assumption spherical symmetric static spacetime existence Killing symmetry to get more acceptable ast...

Abstract A model for inventory systems with multiple products is studied. Demands of items are time-dependent and follow power patterns. Shortages allowed fully backlogged. For this system, our findings provide the efficient policy that helps decision-makers to obtain initial levels reorder points maximize profit per unit time. Moreover, when it assumed warehouse used storage has a limited capa...

The purpose of this paper is to evaluate the revenue efficiency in the fuzzy network data envelopment analysis‎. ‎Precision measurements in real-world data are not practically possible‎, ‎so assuming that data is crisp in solving problems is not a valid assumption‎. ‎One way to deal with imprecise data is fuzzy data‎. ‎In this paper‎, ‎linear ranking functions are used to transform the full fuz...

Although several papers have studied no-idle scheduling problems, they all focus on flow shops, assuming one processor at each working stage. But, companies commonly extend to hybrid flow shops by duplicating machines in parallel in stages. This paper considers the problem of scheduling no-idle hybrid flow shops. A mixed integer linear programming model is first developed to mathematically form...