Although dry farming is important in Azerbaijan, Kurdistan, and Khorasan, as well as some other districts, a large proportion of Iran’s agriculture has always depended upon irrigation. Approximately half the annual grain crop, and an overwhelming proportion of other crops, are irrigated. With the exception of the Caspian littoral almost the whole of Iran is classified as semi-arid or arid. As i...

The culminating philosophy and practice for Buddhist traditions in Tibet is what is found in tantra, or Vajray ā na. Yet Tibet is unique in the Buddhist world in that it is a place where not only the traditions of tantra (for which it is widely known) are practiced, but where the epistemological traditions of valid cognition ( pram āṇ a ) and what came to be known as Pr ā sa ṅ gika-Madhyamaka a...

A collection C of finite L-structures is a 1-dimensional asymptotic class if for every m ∈ N and every formula φ(x, ȳ), where ȳ = (y1, . . . , ym): (i) There is a positive constant C and a finite set E ⊂ R>0 such that for every M ∈ C and ā ∈ Mm, either |φ(M, ā)| ≤ C, or for some μ ∈ E, ∣∣|φ(M, ā)| − μ|M |∣∣ ≤ C|M | 2 . (ii) For every μ ∈ E, there is an L-formula φμ(ȳ), such that φμ(M) is precis...

A theory with the strict order property does not eliminate hyperimaginaries. Hence a theory without the independence property eliminates hyperimaginaries if and only if it is stable. A type definable equivalence relation is an equivalence relation on tuples of a certain length (possibly infinite) which is defined by a partial type E(x̄; ȳ) over ∅. A hyperimaginary is an equivalence class ā/E. If...

5.1. Proof of results in Section 3.1. Under degree-corrected block models, let us denote by Ā the conditional expectation of A given the degree parameters θ = (θ1, ..., θn) T . Note that if θi ≡ 1 then Ā = EA. Since Ā depends on θ, its eigenvalues and eigenvectors may not have a closed form. Nevertheless, we can approximate them using ρi and ūi from Lemma 3. To do so, we need the following lemma.

Given an arbitrary graph G, we study the basic covers algebra Ā(G), which is the symbolic fiber cone of the Alexander dual of the edge ideal of G. Extending results of Villarreal and Benedetti–Constantinescu–Varbaro, valid only in the case when G is bipartite, we characterize in a combinatorial fashion the situations when: 1) Ā(G) is a domain, and 2) Ā(G) is a domain and in addition (the edge i...

In this paper we prove a long-standing conjecture in the theory of twoweight norm inequalities. To state the conjecture and our result we recall a few facts about Orlicz spaces; see [3, Chapter 5] for complete details. Given a Young function A, the complementary function Ā is the Young function that satisfies t ≤ A−1(t)Ā−1(t) ≤ 2t, t > 0. We will say that a Young function Ā satisfies the B2 con...

In this article I argue against Bošković and Takahashi’s (1998) analysis of scrambling as base generation (with lowering for Ā-cases). I present evidence from Russian of scope and antireconstruction effects and scrambling/wh-movement parallels, all implicating a ‘‘classical’’ overt movement account of Ā-scrambling. I then discuss theoretical issues unresolved by the base generation/lowering acc...

In this article, we introduce and study a new class c0 (M, (X, ||.||), ā, ᾱ) of normed space ||.||) valued difference sequences with the help Orlicz function M . This is generalization classical sequence c0. Our primary interest to explore some linear structures investigate conditions relating containment relation in terms different ā ᾱ.

There is a very close and well-understood relationship between proofs in intuitionistic logic, simply typed lambda-terms, and morphisms in Cartesian closed categories. The same relationship can be established for multiplicative linear logic (MLL), where proof nets take the role of the lambda-terms, and starautonomous categories the role of Cartesian closed categories. It is certainly desirable ...