The effect of extreme confinement on the nonlinear-optical response of quantum wires

This work focuses on understanding the nonlinear-optical response of a 1-D quantum wire embedded in 2-D space when quantum-size effects in the transverse direction are minimized using an extremely weighted delta function potential. Our aim is to establish the fundamental basis for understanding the effect of geometry on the nonlinear-optical response of quantum loops that are formed into a network of quantum wires. Using the concept of leaky quantum wires, it is shown that in the limit of full confinement, the sum rules are obeyed when the transverse infinite-energy continuum states are included. While the continuum states associated with the transverse wavefunction do not contribute to the nonlinear optical response, they are essential to preserving the validity of the sum rules. This work is a building block for future studies of nonlinear-optical enhancement of quantum graphs (which include loops and bent wires) based on their geometry. These properties are important in quantum mechanical modeling of any response function of quantum-confined systems, including the nonlinear-optical response of any system in which there is confinement in at leat one dimension, such as nanowires, which provide confinement in two dimensions

Pairwise weakly Hausdorff spaces

summary:In this paper, we introduce and investigate the notion of weakly Hausdorffness in bitopological spaces by using the convergent of nets. Several characterizations of this notion are given. Some relationships between these spaces and other spaces satisfying some separation axioms are studied

Nonuniform Reductions and NP-Completeness

Nonuniformity is a central concept in computational complexity with powerful connections to circuit complexity and randomness. Nonuniform reductions have been used to study the isomorphism conjecture for NP and completeness for larger complexity classes. We study the power of nonuniform reductions for NP0completeness, obtaining both separations and upper bounds for nonuniform completeness vs uniform complessness in NP. Under various hypotheses, we obtain the following separations: 1. There is a set complete for NP under nonuniform many-one reductions, but not under uniform many-one reductions. This is true even with a single bit of nonuniform advice. 2. There is a set complete for NP under nonuniform many-one reductions with polynomial-size advice, but not under uniform Turing reductions. That is, polynomial nonuniformity is stronger than a polynomial number of queries. 3. For any fixed polynomial p(n), there is a set complete for NP under uniform 2-truth-table reductions, but not under nonuniform many-one reductions that use p(n) advice. That is, giving a uniform reduction a second query makes it more powerful than a nonuniform reduction with fixed polynomial advice. 4. There is a set complete for NP under nonuniform many-one reductions with polynomial ad- vice, but not under nonuniform many-one reductions with logarithmic advice. This hierarchy theorem also holds for other reducibilities, such as truth-table and Turing. We also consider uniform upper bounds on nonuniform completeness. Hirahara (2015) showed that unconditionally every set that is complete for NP under nonuniform truth-table reductions that use logarithmic advice is also uniformly Turing-complete. We show that under a derandomization hypothesis, the same statement for truth-table reductions and truth-table completeness also holds

Autoreducibility of NP-Complete Sets

We study the polynomial-time autoreducibility of NP-complete sets and obtain separations under strong hypotheses for NP. Assuming there is a p-generic set in NP, we show the following: - For every $k \geq 2$, there is a $k$-T-complete set for NP that is $k$-T autoreducible, but is not $k$-tt autoreducible or $(k-1)$-T autoreducible. - For every $k \geq 3$, there is a $k$-tt-complete set for NP that is $k$-tt autoreducible, but is not $(k-1)$-tt autoreducible or $(k-2)$-T autoreducible. - There is a tt-complete set for NP that is tt-autoreducible, but is not btt-autoreducible. Under the stronger assumption that there is a p-generic set in NP $\cap$ coNP, we show: - For every $k \geq 2$, there is a $k$-tt-complete set for NP that is $k$-tt autoreducible, but is not $(k-1)$-T autoreducible. Our proofs are based on constructions from separating NP-completeness notions. For example, the construction of a 2-T-complete set for NP that is not 2-tt-complete also separates 2-T-autoreducibility from 2-tt-autoreducibility

On supra R-open sets and some applications on topological spaces

In the present paper a new class of generalized supra open sets called supra R-open set is introduced. The relationships between some generalized supra open sets and this class are investigated and illustrated with enough examples. Also, new types of supra continuous maps, supra open maps, supra closed maps, and supra homeomorphism maps are studied depending on the concept of supra R-open sets. Finally, new separation axioms are dened and their several properties are studied

Using the renal pelvis flap to replace the whole hypoplastic ureter: a preliminary report

Background Hypoplastic ureter is a rare condition usually associated with hypoplastic kidney, and it ends with nephrectomy in most of the cases. Many techniques have been described as ureteric substitutes in the literature. Here, we describe a new technique using the renal pelvis flap to replace the whole hypoplastic ureter in two cases. Objective The aim of this study was to describe a new surgical technique in the management of ureteric hypoplasia.Patients and methods Of the two boys diagnosed antenatally, unilateral hydronephrosis was detected in one boy and a huge renal cyst was present in the other, with evidence of postnatal progressive obstruction necessitating surgical intervention. On exploration, hypoplastic ureter throughout its entire length was an accidental intraoperative finding. The renal pelvis flap was taken and tubularized to replace the entire ureter, and reimplanted into the urinary bladder. This technique was the primary procedure in one case, whereas it was the secondary procedure in the other case after failure of initial trial of pyeloplasty.Results The postoperative period was uneventful with adequate drainage of the renal pelvis in the short-term follow-up (6 and 3 months consecutively).Conclusion The renal pelvis flap is a new feasible alternative procedure for ureteric replacement in a hypoplastic ureter when there is preserved renal parenchyma.Keywords: renal pelvis flap, ureteral hypoplasia, ureteric replacemen

Quantum group symmetry of the Quantum Hall effect on the non-flat surfaces

After showing that the magnetic translation operators are not the symmetries of the QHE on non-flat surfaces , we show that there exist another set of operators which leads to the quantum group symmetries for some of these surfaces . As a first example we show that the $su(2)$ symmetry of the QHE on sphere leads to $su_q(2)$ algebra in the equator . We explain this result by a contraction of $su(2)$ . Secondly , with the help of the symmetry operators of QHE on the Pioncare upper half plane , we will show that the ground state wave functions form a representation of the $su_q(2)$ algebra .Comment: 8 pages,latex,no figur

Power Line Communications: An Overview - Part I

We give an overview of the power line communications (PLC) technology, its importance, its standards and an overview of the HomePlug standards associated with it. This is done is two parts due to publication constraints. In this part, we will concentrate on the PLC applications and the technical issues regarding it. We will also see the layers and methods that are needed to make it work

Variable clinical phenotype in TBK1 mutations: case report of a novel mutation causing primary progressive aphasia and review of the literature

TBK1 mutations are a recently discovered cause of disorders in the frontotemporal dementia (FTD)-amyotrophic lateral sclerosis (ALS) spectrum. We describe a novel L683* mutation, predicted to cause a truncated protein and therefore be pathogenic, in a patient presenting with nonfluent variant primary progressive aphasia (PPA) at the age of 65. Her disease progressed over the following years, leading to her being mute and wheelchair bound seven years into her illness. Brain imaging showed asymmetrical left-sided predominant atrophy affecting the frontal, insular and temporal cortices as well as the striatum in particular. Review of the literature found 60 different nonsense, frameshift, deletion or splice site mutations, including the newly described mutation, with data on clinical diagnosis available in 110 people: 58% of the cases presented with an ALS syndrome, 16% with an FTD-ALS overlap, 19% with a cognitive presentation (including behavioural variant FTD (bvFTD) and PPA) and 4% with atypical parkinsonism. Age at onset (AAO) data was available in 75 people: mean (standard deviation) AAO was 57.5 (10.3) in those with ALS, which was significantly younger than those with a cognitive presentation (AAO = 65.1 (10.5), p = 0.008), or atypical parkinsonism (AAO = 68.3 (8.7), p = 0.021), with a trend compared with the FTD-ALS group (AAO = 61.9 (7.0), p=0.065); there was no significant difference in AAO between the other groups. In conclusion, clinical syndromes across the whole FTD-ALS-atypical parkinsonism spectrum have been reported in conjunction with mutations in TBK1. It is therefore important to include TBK1 on future gene panels for each of these disorders, and to suspect such mutations particularly when there are multiple different phenotypes in the same family