Super congruences and Euler numbers

Let $p>3$ be a prime. We prove that $$\sum_{k=0}^{p-1}\binom{2k}{k}/2^k=(-1)^{(p-1)/2}-p^2E_{p-3} (mod p^3),$$ $$\sum_{k=1}^{(p-1)/2}\binom{2k}{k}/k=(-1)^{(p+1)/2}8/3*pE_{p-3} (mod p^2),$$ $$\sum_{k=0}^{(p-1)/2}\binom{2k}{k}^2/16^k=(-1)^{(p-1)/2}+p^2E_{p-3} (mod p^3)$$, where E_0,E_1,E_2,... are Euler numbers. Our new approach is of combinatorial nature. We also formulate many conjectures concerning super congruences and relate most of them to Euler numbers or Bernoulli numbers. Motivated by our investigation of super congruences, we also raise a conjecture on 7 new series for $\pi^2$, $\pi^{-2}$ and the constant $K:=\sum_{k>0}(k/3)/k^2$ (with (-) the Jacobi symbol), two of which are $$\sum_{k=1}^\infty(10k-3)8^k/(k^3\binom{2k}{k}^2\binom{3k}{k})=\pi^2/2$$ and $$\sum_{k>0}(15k-4)(-27)^{k-1}/(k^3\binom{2k}{k}^2\binom{3k}k)=K.$

Oral Interview of Wilbur Mortenson

Mr. Mortenson has been a member of the American Legion since 1946. He discusses the Legion\u27s history, goals and purposes.https://red.mnstate.edu/oral_interviews/1196/thumbnail.jp

Secondary structure of Ac-Alan_n-LysH+^+ polyalanine peptides (nn=5,10,15) in vacuo: Helical or not?

The polyalanine-based peptide series Ac-Ala_n-LysH+ (n=5-20) is a prime example that a secondary structure motif which is well-known from the solution phase (here: helices) can be formed in vacuo. We here revisit this conclusion for n=5,10,15, using density-functional theory (van der Waals corrected generalized gradient approximation), and gas-phase infrared vibrational spectroscopy. For the longer molecules (n=10,15) \alpha-helical models provide good qualitative agreement (theory vs. experiment) already in the harmonic approximation. For n=5, the lowest energy conformer is not a simple helix, but competes closely with \alpha-helical motifs at 300K. Close agreement between infrared spectra from experiment and ab initio molecular dynamics (including anharmonic effects) supports our findings.Comment: 4 pages, 4 figures, Submitted to JPC Letter

Creative destruction over the business cycle: a stochastic frontier analysis

[[abstract]]This paper examines the within-industry distributions of jobs created and destructed across plants in terms of technical efficiency, technical efficiency change, scale effect, and technical change. It further investigates how these distributions vary with economic activity. By applying the stochastic frontier analysis to plant-level longitudinal data on Taiwan’s 23 two-digit manufacturing industries spanning the period 1992–2003, we find that jobs created (destructed) are disproportionately clustered at plants with lower technical efficiency but higher rate of technical change. A fall in economic activities is associated with a statistically significant decrease (increase) in the fraction of newly created (destructed) jobs accounted for by plants with a higher rate of technical change, indicating that creative destruction is more pronounced during economic contractions.[[journaltype]]國外[[incitationindex]]SSCI[[ispeerreviewed]]Y[[countrycodes]]US

Biophysical, Grazing-Season Management, and Animal Traits Effects on Individual Animal Performance of Cow-Calf Systems: Insights from a Long-Term Experiment in the US Western Great Plains

Beef grazing systems require information on management, biophysical, and individual animal influences on performance metrics. However, long-term controlled experiments are lacking to comprehensively ascertain these individual and likely interacting influences. We used a legacy data set from the USDA Agricultural Research Service where individual weight gains were determined from on and off weights of Hereford cows and calves grazing native northern mixed-grass prairie, during the June through September season, from 1975-2001 near Cheyenne, Wyoming, USA. The herd size varied from a minimum of 10 to a maximum of 48 pairs across years. Management (on and off grazing dates and stocking rate, kg BW/ha), biophysical (forage production estimated through NDVI LANDSAT time series, temperature, and precipitation variability), and individual animal (cow age, cow body weight at beginning of grazing season, and calf gender) influences were evaluated for effects on calf weight gain (WG, kg/head). Linear mixed models were used for analyses where the above mentioned were fixed factors, and year and individual cow were random ones. Calf performance was influenced by three animal traits: gender with steer WG 4 kg more than heifer, cow body weight with calf WG increased 2kg for each 100kg of cow body weight, and cow age as optimum calf WG occurred with 5-year-old cows. Management influenced calf WG through the on and off dates. Delaying the start of a grazing season decreased calf WG by 0.80 kg per delayed day. On the contrary, extending the grazing season increased calf WG by about the same amount. Biophysical effects on calf WG were not significant suggesting that the cow performance was mitigating these effects of variability. Results suggest that calf individual performance in this resilient rangeland ecosystem relies on cows’ body weight at beginning of the grazing, their age, and the timing to enter and remove animals from pastures

Specific orofacial problems experienced by musicians

Background: Patients who play musical instruments (especially wind and stringed instruments) and vocalists are prone to particular types of orofacial problems. Some problems are caused by playing and some are the result of dental treatment. This paper proposes to give an insight into these problems and practical guidance to general practice dentists. Method: Information in this paper is gathered from studies published in dental, music and occupational health journals, and from discussions with career musicians and music teachers. Results: Orthodontic problems, soft tissue trauma, focal dystonia, denture retention, herpes labialis, dry mouth and temporomandibular joint (TMJ) disorders were identified as orofacial problems of career musicians. Options available for prevention and palliative treatment as well as instrument selection are suggested to overcome these problems. Conclusions: Career musicians express reluctance to attend dentists who are not sensitive to their specific needs. General practitioner dentists who understand how the instruments impact on the orofacial structures and are aware of potential problems faced by musicians are able to offer preventive advice and supportive treatment to these patients, especially those in the early stages of their career

Proteasome Inhibitors Block DNA Repair and Radiosensitize Non-Small Cell Lung Cancer

Despite optimal radiation therapy (RT), chemotherapy and/or surgery, a majority of patients with locally advanced non-small cell lung cancer (NSCLC) fail treatment. To identify novel gene targets for improved tumor control, we performed whole genome RNAi screens to identify knockdowns that most reproducibly increase NSCLC cytotoxicity. These screens identified several proteasome subunits among top hits, including the topmost hit PSMA1, a component of the core 20 S proteasome. Radiation and proteasome inhibition showed synergistic effects. Proteasome inhibition resulted in an 80–90% decrease in homologous recombination (HR), a 50% decrease in expression of NF-κB-inducible HR genes BRCA1 and FANCD2, and a reduction of BRCA1, FANCD2 and RAD51 ionizing radiation-induced foci. IκBα RNAi knockdown rescued NSCLC radioresistance. Irradiation of mice with NCI-H460 xenografts after inducible PSMA1 shRNA knockdown markedly increased murine survival compared to either treatment alone. Proteasome inhibition is a promising strategy for NSCLC radiosensitization via inhibition of NF-κB-mediated expression of Fanconi Anemia/HR DNA repair genes.American Society for Radiation Oncology (Junior Faculty Career Research Training Award)Harvard University. Joint Center for Radiation Therapy (Foundation Grant)Dana-Farber/Harvard Cancer Center (SPORE Developmental Research Project Award in Lung Cancer Research)National Cancer Institute (U.S.) (Award K08CA172354

Quantitative Trait Loci (QTL) for Forage Traits in Intermediate Wheatgrass When Grown as Spaced-Plants versus Monoculture and Polyculture Swards

It has been hypothesized that the genetic control of forage traits, especially biomass, for grass plants growing as spaced-plants versus swards is different. Likewise, the genetic control of compatibility in grass–legume polyculture mixtures is assumed to be different than for forage production in a grass monoculture. However, these hypotheses are largely unvalidated, especially at the DNA level. This study used an intermediate wheatgrass mapping population to examine the effect of three competition environments (spaced-plants, polyculture, and monoculture) on classical quantitative genetic parameters and quantitative trait loci (QTL) identification for biomass, morphology, and forage nutritive value. Moderate to high heritable variation was observed for biomass, morphological traits, and nutritive value within all three environments (H ranged from 0.50 to 0.87). Genetic correlations (rG) among environments for morphology and nutritive value were predominantly high, however, were moderately-low (0.30 to 0.48) for biomass. Six biomass QTL were identified, including three on linkage groups (LG) 1, 6, and 15 that were only expressed in the monoculture environment. Moreover, three biomass QTL on LG 10, 14, and 15 exhibited significant QTL by environment interactions. This study verified that the genetic control of grass biomass in a monoculture versus a grass–legume mixture is only partially the same, with additional genes expressed in monoculture, and that biomass in widely spaced-plants versus swards is predominantly under different genetic control. These results indicate that selection for improved grass biomass will be most successful when conducted within the targeted monoculture or polyculture sward environment per se