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In this paper, we establish the explicit lower bound estimates for the rank of universal quadratic forms in some certain families of real cubic fields under the condition of density one. The more general results that represent all multiples of a given rational integer are obtained for totally positive definite quadratic lattices. Our main tools are some properties of indecomposable integers with trace in these fields and short vectors in quadratic lattices.

The rapid progress of interdisciplinary researches from materials science, biotechnologies, biomedical engineering, and medicine, have resulted in the emerging of bioinspired skins for various fantasticating applications. Bioinspired skin is highly promising in the application of rehabilitation medicine owing to their advantages, including personalization, excellent biocompatibility, multi-functionality, easy maintainability and wearability, and mass production. Therefore, this review presents the recent progress of bioinspired skin towards next-generation rehabilitation medicine. The classification is first briefly introduced. Then, various applications of bioinspired skins in the field of rehabilitation medicine at home and abroad are discussed in detail. Last, we provide the challenges we are facing now, and propose the next research directions.

Let $b_k(n)$ denote the $k-$regular partitons of a natural number $n$. In this paper, we study the behavior of $b_k(n)$ modulo composite integers $M$ which are coprime to $6$. Specially, we prove that for arbitrary $k-$regular partiton function $b_k(n)$ and integer $M$ coprime to $6$, there are infinitely many Ramanujan-type congruences of $b_k(n)$ modulo $M$.

We study the parity of rank of $2$-${\rm Selmer}$ groups associated to $\pi/3$ and $2\pi/3$-congruent numbers. Our second result gives some positive densities about $\pi/3$ and $2\pi/3$ non-congruent numbers which can support the even part of Goldfeld's conjecture. We give some necessary conditions such that $n$ is non $\pi/3$-congruent number for elliptic curves $E_n$ whose Shafarevich-Tate group is non-trivial. In the last section, we show that for $n=pq\equiv 5(resp. \ 11)\pmod{24}$, the density of non $\pi/3$($resp.$ $2\pi/3$)-congruent numbers is at least 75\%, where $p,q$ are primes.

We derive 10 new Ramanujan-Sato series of $1/\pi$ by using the method of Huber, Schultz and Ye. The levels of these series are 14, 15, 16, 20, 21, 22, 26, 35, 39.

ObjectiveTo precisely determine the species of a carbapenem-resistant Pseudomonas strain 1809276 isolated from the urine of a Chinese patient and analyze its integrative and conjugative element (ICE) 1276 formation mechanism.MethodsSingle-molecule real-time (SMRT) sequencing was carried out on strain 18091276 to obtain the complete chromosome and plasmid (pCN1276) sequences, and average nucleotide identity (ANI) was used for precise species identification. The ICEs in GenBank with the same integrase structure as ICE 1276 were aligned. At the same time, the transfer ability of blaIMP−1 and the antibiotic sensitivity of Pseudomonas juntendi 18091276 were tested.ResultsThis bacterium was P. juntendi, and its drug resistance mechanism is the capture of the accA4' gene cassette by the Tn402-like type 1 integron (IntI1-blaIMP−1) to form In1886 before its capture by the ΔTn4662a-carrying ICE 1276. The acquisition of blaIMP−1 confers carbapenem resistance to P. juntendi 18091276.ConclusionThe formation of blaIMP−1-carrying ICE 1276, its further integration into the chromosomes, and transposition and recombination of other elements promote bacterial gene accumulation and transmission.

Additional file 3. The original western blot images of β-actin.

Additional file 1. Original western blot images in the text.

We derive 10 new Ramanujan-Sato series of $1/π$ by using the method of Huber, Schultz and Ye. The levels of these series are 14, 15, 16, 20, 21, 22, 26, 35, 39.

By a formula of Villegas, the Mahler measures of $P_k(x,y)=x+1/x+y+1/y+k$ can be written as a Kronecker-Eisenstein series, where $k=\frac{4}{\sqrt{\lambda(2\tau)}}$ and $\lambda(\tau)=16\frac{\eta(\tau/2)^8\eta(2\tau)^{16}}{\eta(\tau)^{24}}$ is the modular lambda-function. If $\tau$ is taken to be CM points, we can use Villegas's formula to express the Mahler measures of $P_k$ as $L$-values of some modular forms. We prove that if $\tau_0$ is a CM point, then $\lambda(2\tau_0)$ is an algebraic number whose degree can be bounded by the product of the class numbers of $D_{\tau_0}$ and $D_{4\tau_0}$, where $D_{\tau}$ stands for the discriminant of a CM point $\tau$. Then we use the CM points with class numbers $\leqslant 2$ to obtain identities linking the Mahler measures of $P_k$ to $L$-values of modular forms. We get 35 identities, 5 of which are proven results, the others do not seem to appear in the literature. We also verify some cases of Beilinson's conjecture for elliptic curves over real quadratic fields that related to our discovery. Our method might also be used to other polynomial familys that mentioned in Villegas's paper.

We study the parity of rank of $2$-${\rm Selmer}$ groups associated to $π/3$ and $2π/3$-congruent numbers. Our second result gives some positive densities about $π/3$ and $2π/3$ non-congruent numbers which can support the even part of Goldfeld's conjecture. We give some necessary conditions such that $n$ is non $π/3$-congruent number for elliptic curves $E_n$ whose Shafarevich-Tate group is non-trivial. In the last section, we show that for $n=pq\equiv 5(resp. \ 11)\pmod{24}$, the density of non $π/3$($resp.$ $2π/3$)-congruent numbers is at least 75\%, where $p,q$ are primes.

Additional file 2. MSCs characterization.

We improve S.-C. Chen's result on the parity of Schur's partition function. Let $A(n)$ be the number of Schur's partitions of $n$, i.e., the number of partitions of $n$ into distinct parts congruent to $1, 2 \mod{3}$. S.-C. Chen \cite{MR3959837} shows $\small \frac{x}{(\log{x})^{\frac{47}{48}}} \ll \sharp \{0\le n\le x:A(2n+1)\; \text{is odd}\}\ll \frac{x}{(\log{x})^{\frac{1}{2}}}$. In this paper, we improve Chen's result to $\frac{x}{(\log{x})^{\frac{11}{12}}} \ll \sharp \{0\le n\le x:A(2n+1)\; \text{is odd}\}\ll \frac{x}{(\log{x})^{\frac{1}{2}}}.$

Additional file 1: Fig. S1. Establishment of T2D-associated NAFLD mouse model. (A) The body weight monitoring of mice fed with HFD or ND from 6th week to 32nd week. (B) The detection of serum insulin at 32nd week. (C) The GTT and ITT assay at 32nd week. (D) The detection of serum ALT and AST at 32nd week. All statistical data are represented as means �� s. *P

We study the 2-adic behavior of the number of domino tilings of a $2(2n+1)\times 2(2n+1)$ torus. We show that this number is of the form $2^{4n+3}g(n)^2+2^{8n+2}(2n+1)^{4n}h(n)$, where $g(n)$ and $h(n)$ are odd positive integers. Moreover, we prove that $g(n)$ and $h(n)$ are uniformly continuous under the 2-adic metric and invariant under interchanging $n$ and $-1-n$. This paper is an analogy of Henry Cohn's results for $2n\times 2n$ squares (Electron. J. Combin. 6 (1999))., Contributions to Discrete Mathematics, Vol 14 No 1 (2019)

Rationale: Primary malignant melanoma of the lung (PMML) is an extremely rare neoplasm with a dismal prognosis. The diagnosis of PMML is very difficult and is based on several clinical, radiological, and histopathological criteria. Patient concerns: A 61-year-old women was admitted with a 2-month history of a productive cough and chest pain provoked by breathing and coughing. Computed tomography (CT) scans of the chest showed a large, solid tumor in the right middle lobe of the lung. Puncture biopsy of the right lung lesion was performed using B-ultrasound guidance, and immunohistochemical tests were performed. Diagnoses: The diagnosis of PMML was histopathologically confirmed by puncture biopsy with B-ultrasound guidance of the right lung lesion. Interventions: The patient refused to receive surgery, adjuvant chemotherapy, or radiation therapy. Outcomes: The patient died 6 months after the diagnosis. Lessons: The clinical manifestation and imaging features of PMML are not specific, and it does not differ from the more common primary bronchogenic carcinoma. In addition, it cannot be discriminated from other forms of primary melanoma according to its histology and immunohistochemistry. The treatment of choice is an aggressive surgical approach, combined with radiation therapy, chemotherapy, and immunotherapy.

Obviously, the so-called “Twenty years of political amnesia” refer to the years before Hitler governed Germany and the years governed by Hitler. The time is named “the period of the Nazi” by historians or declared “the era of the fatherless” by some psychologist. Indeed, many films produced in the 1960s and early 1970s avoid reference to the events of the nearly two decades of Nazi-rule on purpose. With the climax of the New German Cinema, a number of directors and filmmakers bravely embraced the fatherless society. Obviously, the so-called “Twenty years of political amnesia” refer to the years before Hitler governed Germany and the years governed by Hitler. The time is named “the period of the Nazi” by historians or declared “the era of the fatherless” by some psychologist. Indeed, many films produced in the 1960s and early 1970s avoid reference to the events of the nearly two decades of Nazi-rule on purpose. With the climax of the New German Cinema, a number of directors and filmmakers bravely embraced the fatherless society.

Expeditions during the summers of 2002 and 2003 implemented continuous monitoring of near-surface (2 m height) atmospheric CO2 and H2O concentrations at the 4500 m elevation on Muztagata. The resultant data sets reveal a slight decrease of CO2 concentrations (of about 5 μmol·mol-1) and changes in the diurnal variations from the end of June to the middle August. The daily maximum CO2 concentrations occur between 02:30-05:30 AM (local time) and the minimum levels occur between 12:00-15:30 PM. The atmospheric CO2 concentrations in the summer of 2002 were around 5 μmol·mol-1 lower than those during the same period of 2003, whereas the diurnal amplitude was higher. In contrast, we found that the daily mean atmospheric H2O content in 2003 was much lower than that in 2002 and there exists a striking negative correlation between CO2 and H2O concentrations. We therefore suggest that the near-surface atmospheric CO2 concentration is affected not only by photosynthesis and respiration, but also by the air H2O content in the glaciated region around Muztagata.