A q-Analog of Dual Sequences with Applications

In the present paper combinatorial identities involving q-dual sequences or polynomials with coefficients q-dual sequences are derived. Further, combinatorial identities for q-binomial coefficients(Gaussian coefficients), q-Stirling numbers and q-Bernoulli numbers and polynomials are deduced.Comment: 14 page

Why not Merge the International Monetary Fund (IMF) with the International Bank for Reconstruction and Development (World Bank)

Motivation: Cellular Electron CryoTomography (CECT) is an emerging 3D imaging technique that visualizes subcellular organization of single cells at sub-molecular resolution and in near-native state. CECT captures large numbers of macromolecular complexes of highly diverse structures and abundances. However, the structural complexity and imaging limits complicate the systematic de novo structural recovery and recognition of these macromolecular complexes. Efficient and accurate reference-free subtomogram averaging and classification represent the most critical tasks for such analysis. Existing subtomogram alignment based methods are prone to the missing wedge effects and low signal-to-noise ratio (SNR). Moreover, existing maximum-likelihood based methods rely on integration operations, which are in principle computationally infeasible for accurate calculation. Results: Built on existing works, we propose an integrated method, Fast Alignment Maximum Likelihood method (FAML), which uses fast subtomogram alignment to sample sub-optimal rigid transformations. The transformations are then used to approximate integrals for maximum-likelihood update of subtomogram averages through expectation-maximization algorithm. Our tests on simulated and experimental subtomograms showed that, compared to our previously developed fast alignment method (FA), FAML is significantly more robust to noise and missing wedge effects with moderate increases of computation cost. Besides, FAML performs well with significantly fewer input subtomograms when the FA method fails. Therefore, FAML can serve as a key component for improved construction of initial structuralmodels frommacromolecules captured by CECT

Advance Selling in the Presence of Experienced Consumers

The advance selling strategy is implemented when a firm offers consumers the opportunity to order its product in advance of the regular selling season. Advance selling reduces uncertainty for both the firm and the buyer and enables the firm to update its forecast of future demand. The distinctive feature of the present theoretical study of advance selling is that we divide consumers into two groups, experienced and inexperienced. Experienced consumers know their valuations of the product in advance. The presence of experienced consumers yields new insights. Specifically, pre-orders from experienced consumers lead to a more precise forecast of future demand by the firm. We show that the firm will always adopt advance selling and that the optimal pre-order price may or may not be at a discount to the regular selling price.advance selling, the Newsvendor Problem, demand uncertainty, experienced consumers, inexperienced consumers.

Earthquake Induced Displacement of Gravity Retaining Walls

Centrifuge tests were conducted to study the displacement of gravity retaining walls during earthquakes. Theoretical analysis based on Newmark\u27s sliding block method was used to analyze the data. For a gravity wall with dry backfill, sliding block method generates reasonable results. However, the method is difficult to apply for a retaining wall with saturated backfill. Comprehensive numerical methods need to be used. A method of calculating the tilting of gravity walls is introduced

Quantum Capacities for Entanglement Networks

We discuss quantum capacities for two types of entanglement networks: $\mathcal{Q}$ for the quantum repeater network with free classical communication, and $\mathcal{R}$ for the tensor network as the rank of the linear operation represented by the tensor network. We find that $\mathcal{Q}$ always equals $\mathcal{R}$ in the regularized case for the samenetwork graph. However, the relationships between the corresponding one-shot capacities $\mathcal{Q}_1$ and $\mathcal{R}_1$ are more complicated, and the min-cut upper bound is in general not achievable. We show that the tensor network can be viewed as a stochastic protocol with the quantum repeater network, such that $\mathcal{R}_1$ is a natural upper bound of $\mathcal{Q}_1$. We analyze the possible gap between $\mathcal{R}_1$ and $\mathcal{Q}_1$ for certain networks, and compare them with the one-shot classical capacity of the corresponding classical network

The effects of clinical dental status on eating difficulty and oral health-related quality of life in an older Chinese population.

Most studies about the relationships between dental status and eating difficulty and food choice have been done in Western countries. Their foods and methods of preparation differ from Eastern countries. Therefore, studies are required in countries such as China to assess whether the findings are universal.;Hypothesis: Clinical dental status significantly affects eating difficulty and oral health-related quality of life in older Chinese people.;The main objectives were to: 1. Develop an Index of Eating Difficulty (IED) 2. Assess prevalence and severity of eating difficulties and relationship between clinical dental status and eating difficulties, and 3. Assess prevalence and severity of oral impacts on oral health-related quality of daily life and the relationship between clinical dental status and oral health-related quality of life using the Oral Impacts on Daily Performances (OIDP) measure of impact.;Methods: The study was done in Nanning city, Guangxi province, China. Subjects were 1229 older people aged 55 to 100 years from the Routine check-ups Centre of Guangxi Medical University Hospital. Subjects were clinically examined and replied to questionnaires. The IED based on Chinese foods was developed and validated. The OIDP was validated.;Findings: 51.8% of dentate subjects had general eating difficulty. Ease of eating certain foods was related to the numbers of teeth, occluding pairs and unfilled spaces. There were significant relationships between clinical dental status and IED in both unadjusted and adjusted models. Clinical dental status was also significantly related to general eating difficulty and dissatisfaction with chewing ability. There were significant relationships between clinical dental status and the overall OIDP score as well as the prevalence of the OIDP eating impact.;Conclusions: The findings of this research support the hypothesis of this study and indicate that clinical dental status significantly influenced eating difficulty and quality of life in a sample of older Chinese population in Guangxi province, China

The Degasperis-Procesi equation with self-consistent sources

The Degasperis-Procesi equation with self-consistent sources(DPESCS) is derived. The Lax representation and the conservation laws for DPESCS are constructed. The peakon solution of DPESCS is obtained.Comment: 15 page