Roman Model-Books as a Resource for Digital Architectural Reconstructions

Upon examination of Roman landscape paintings preserved in situ and in museums of Naples and Rome, additional evidence has been found for the additive character of creation of imaginary landscapes as well as evidence for using standardized elements and whole scene compositions in Roman painting. This attitude is compared to the modern way of creating virtual landscapes—computer game level design and the process called “kitbashing”. I propose that both these processes share the same task to create a familiar landscape using a visual language understandable to its contemporary viewer, but also a very similar method of using predefined elements.

Mathematical Modeling Shows That the Response of a Solid Tumor to Antiangiogenic Therapy Depends on the Type of Growth

It has been hypothesized that solid tumors with invasive type of growth should possess intrinsic resistance to antiangiogenic therapy, which is aimed at cessation of the formation of new blood vessels and subsequent shortage of nutrient inflow to the tumor. In order to investigate this effect, a continuous mathematical model of tumor growth is developed, which considers variables of tumor cells, necrotic tissue, capillaries, and glucose as the crucial nutrient. The model accounts for the intrinsic motility of tumor cells and for the convective motion, arising due to their proliferation, thus allowing considering two types of tumor growth—invasive and compact—as well as their combination. Analytical estimations of tumor growth speed are obtained for compact and invasive tumors. They suggest that antiangiogenic therapy may provide a several times decrease of compact tumor growth speed, but the decrease of growth speed for invasive tumors should be only modest. These estimations are confirmed by numerical simulations, which further allow evaluating the effect of antiangiogenic therapy on tumors with mixed growth type and highlight the non-additive character of the two types of growth.

Improved bounds on Gauss sums in arbitrary finite fields

Let [Formula: see text] be a power of a prime and let [Formula: see text] be the finite field consisting of [Formula: see text] elements. We establish new explicit estimates on Gauss sums of the form [Formula: see text], where [Formula: see text] is a nontrivial additive character. In particular, we show that one has a nontrivial upper bound on [Formula: see text] for certain values of [Formula: see text] of order up to [Formula: see text]. Our results improve on the previous best-known bound due to Zhelezov.

Large family of pseudorandom subsets of the set of the integers not exceeding N

In a series of papers, Dartyge and Sárközy (partly with other coauthors) studied large families of pseudorandom subsets. In this paper, we introduce a new large family of pseudorandom subsets constructed by the multiplicative inverse and additive character, and study the pseudorandom measures. Furthermore, we extend the family of subsets to the case when the moduli is composite.

ON THREE-VARIABLE EXPANDERS OVER FINITE FIELDS

Let 𝔽q be the finite field with q elements and P(x, y) be a polynomial in 𝔽q[x, y]. Using additive character sum estimates, we study expander property of the function x1 + P(x2, x3). We give an alternative proof using spectra of sum–product graphs in the case of P(x, y) = xy, and also extend the problem in the setting of finite cyclic rings.

G2 Examples: the Overall Strategy

This fixes, for each prime p, a prime 𝓁 ≠ p and a choice of nontrivial ℚ¯ℓX-valued additive character ψ‎ of the prime field 𝔽ₚ. Given a finite extension field k/𝔽ₚ, it takes as nontrivial additive character of k the composition k := ψ‎ ○ Trk/𝔽p, whenever a nontrivial additive character of k is (implicitly or explicitly) called for (for instance in the definition of a Kloosterman sheaf, or of a hypergeometric sheaf, on 𝔾ₘ/k).

SL(n) Examples with Slightly Composite n

This chapter continues to study the object N of Theorem 21.1. Thus, k is a finite field of characteristic p, ψ‎ a nontrivial additive character of k, f(x) = f(x)=∑i=−baAixi∈k[x,1/x]Aᵢxⁱ ɛ k[x, 1/x] is a Laurent polynomial of “bidegree” (a, b), with a; b both ≤ 1 and both prime to p. It is assumed that f(x) is Artin–Schreier reduced. It takes for N the object N:ℒψ(f(x))(1/2)[1]∈ρarith.

Application of Anion Multifunctional Additive in Polymer

The title introduced Anion anionic additive, character and application. Anionic additive can apply in paint, textile, coating, foam, plastic, etc. The structure of opal shale and the mechanism of release anion were discussed. The opal shale was comminuted by the airflow method. The average diameter of the opal shale granule was observed by granularity instrument. The result indicated that size is about 0.40-5.0μm. The printing poplin with high performance was achieved by intermingle technology and the generally printing means. The anion number (4000 ions /cm3) in printing poplin was measured.