The effect of dietary factors on health status has been recognized since antiquity. Although some of the dietary phytochemicals and bioactives have traditionally been considered as “antinutrients”, their beneficial effects in human health promotion and disease prevention has recently been acknowledged. While nutraceuticals, sometimes referred to as natural health products, are often used in med...

This paper proposes a new grocery store layout based on the association among product categories. The very first grocery stores displayed their products in an industrial approach, which have produced the present day grocery store layouts based on “sectors” as fruits, vegetables, magazines, cds, and so on. This approach is company oriented and it fails to respond to the needs of the time-pressur...

Let U/Q be a unitary group of Q-rank one so that the real points U(R)?U(n,1). The U is only quasi-split over Q if and n=1,2. cohomology congruence subgroup closely related to theory automorphic forms. This relation best captured in so-called spaces H?(U,C), natural module under action U(Af). paper gives structural account U(Af)-module structure part which generated by residues or derivatives Ei...

A strong impetus for this paper came, at least for the first author, from a question of Avner Ash, asking whether one can construct non-selfdual, nonmonomial cuspidal cohomology classes for suitable congruence subgroups Γ of SL(n,Z), say for n = 6. Such a construction, in special examples, has been known for some time for n = 3 ([AGG1984], [vGT1994], [vGKTV1997], [vGT2000]); it is of course not...

In addition to being a religious book with high human and moral themes, Nahj al-Balagha is considered mirror of Arab culture literary masterpiece at the height eloquence eloquence, because proverbs in form short, concrete understandable phrases for everyone, experiences, thoughts convey ideas, Imam Ali (AS) used it facilitate understanding various political, social concepts. this article, we in...

We present topics in the Langlands Program to graduate students and a wider mathematically mature audience. study both global local aspects characteristic zero as well p p ...

Let F be a number field with adele ring AF , and let π, π ′ be cuspidal automorphic representations of GL2(AF ), say with the same central character. If the symmetric squares of π and π are isomorphic, we know that π will need to be an abelian, in fact quadratic, twist of π, which amounts to a multiplicity one statement for SL(2) ([Ram1]). It is of interest to ask if the situation is the same f...

The present article was motivated by a question raised independently by Barry Mazur and Nick Katz. The articles [CHT,HST,T] contain a proof of the Sato-Tate conjecture for an elliptic curve E over a totally real field whose j-invariant j(E) is not an algebraic integer. The Sato-Tate conjecture for E is an assertion about the equidistribution of Frobenius angles of E, or equivalently about the n...

Conjecture 1 (Langlands). To each reductive group G over a number field K, each automorphic (complex) representation π of G, and each finite dimensional representation r of the (complex) group G, there is defined an automorphic L-function L(s, π, r), which enjoys an analytic continuation and functional equation generalizing the Riemann zeta function πΓ(s/2)ζ(s) (or Artin’s L-function L(s, σ), w...

In his pioneering work, H. Garland constructed Eisenstein series on affine Kac-Moody groups over the field of real numbers. He established the almost everywhere convergence of these series, obtained a formula for their constant terms, and proved a functional equation for the constant terms. In his subsequent paper, the convergence of the Eisenstein series was obtained. In this paper, we define ...