Results 31 to 40 of about 2,569 (239)

Sum-product estimates in finite fields

, 2006
We prove, using combinatorics and Kloosterman sum technology that if $A \subset {\Bbb F}_q$, a finite field with $q$ elements, and $q^{1/2} \lesssim |A| \lesssim q^{7/10}$, then $\max \{|A+A|, |A \cdot A|\} \gtrsim \frac{{|A|}^{3/2}}{q^{1/4}$.
Hart, D., Iosevich, A., Solymosi, J.
openaire   +2 more sources

Cell geometry and membrane protein crowding constrain Escherichia coli growth rate, overflow metabolism, respiration, and maintenance energy

FEBS Letters, EarlyView.
The physical dimensions and shape of bacterial cells define the surface area available to acquire nutrients and the volume available for synthesizing proteins and DNA. Here, we use computational systems biology to decode the importance of cell geometry as a major determinant of prokaryotic phenotype, including growth rate and metabolic efficiency. This
Ross P. Carlson, Tomáš Gedeon, Mauricio Garcia Benitez, Campbell Putnam, William R. Harcombe, Radhakrishnan Mahadevan, Ashley E. Beck   +6 more
wiley   +1 more source

ON THE SOLVABILITY OF SYSTEMS OF SUM–PRODUCT EQUATIONS IN FINITE FIELDS [PDF]

Glasgow Mathematical Journal, 2011
AbstractIn an earlier paper, for ‘large’ (but otherwise unspecified) subsets , , , of q, Sárközy showed the solvability of the equations a + b = cd with a ∈ , b ∈ , c ∈ , d ∈ . This equation has been studied recently by many other authors. In this paper, we study the solvability of systems of equations of this type using additive character sums.
openaire   +1 more source

A sum-product estimate in finite fields, and applications [PDF]

Geometric And Functional Analysis, 2004
Let $A$ be a subset of a finite field $F := \Z/q\Z$ for some prime $q$. If $|F|^δ< |A| < |F|^{1-δ}$ for some $δ> 0$, then we prove the estimate $|A+A| + |A.A| \geq c(δ) |A|^{1+\eps}$ for some $\eps = \eps(δ) > 0$. This is a finite field analogue of a result of Erdos and Szemeredi.
Bourgain, Jean, Katz, N., Tao, Terence C.   +2 more
openaire   +3 more sources

Optimizing photoexcitation conditions for time‐resolved X‐ray solution scattering experiments

FEBS Open Bio, EarlyView.
Time‐resolved X‐ray solution scattering (TR‐XSS) is a powerful technique to visualize how proteins change their structure in real time after light activation. Selecting the right laser photoexcitation conditions—fluence, excitation geometry, and sample refresh rate—is critical to maximize the experimental signal while avoiding unwanted side effects ...
Matteo Levantino
wiley   +1 more source

Quantum memory assisted observable estimation [PDF]

Quantum
The estimation of many-qubit observables is an essential task of quantum information processing. The generally applicable approach is to decompose the observables into weighted sums of multi-qubit Pauli strings, i.e., tensor products of single-qubit ...
Liubov A. Markovich, Attaallah Almasi, Sina Zeytinoğlu, Johannes Borregaard   +3 more
doaj   +1 more source

On multiple sum and product sets of finite sets of integers

Comptes Rendus. Mathématique, 2003
Let A ⊂ ℤ be a finite set of integers of cardinality | A |= N ⩾2. Given a
Bourgain, Jean, Chang, Mei-Chu
openaire   +1 more source

Normal‐Appearing White Matter Injury Mediates Chronic Deep Venous Hypoxia and Disease Progression in Multiple Sclerosis

Annals of Clinical and Translational Neurology, EarlyView.
ABSTRACT Objective To explore how cerebral hypoxia and Normal‐Appearing White Matter (NAWM) integrity affect MS lesion burden and clinical course. Methods Seventy‐nine MS patients, including 13 clinically isolated syndrome (CIS) patients and 66 relapsing–remitting multiple sclerosis (RRMS) patients, and 44 healthy controls (HCs) were recruited from ...
Xinli Wang, Huiying Wang, Zhizheng Zhuo, Ai Guo, Ke Lv, Decai Tian, Chao Chai, Yunyun Duan, Shuang Xia   +8 more
wiley   +1 more source

Dual Toeplitz Operators on Bounded Symmetric Domains

Mathematics
We give some characterizations of dual Toeplitz operators acting on the orthogonal complement of the Bergman space over bounded symmetric domains. Our main result characterizes those finite sums of products of Toeplitz operators that are themselves dual ...
Jianxiang Dong
doaj   +1 more source

The finite sum of finite products of Toeplitz operators on the polydisk

Journal of Mathematical Analysis and Applications, 2006
This paper gives some connection between the theory of Toeplitz operator theory and function theory of the polydisk, and establishes a limit theorem for a finite sum of finite products of Toeplitz operators on the Hardy space in the polydisk. As a consequence, it shows that the product of six Toeplitz operators with pluriharmonic symbols is compact if ...
openaire   +2 more sources