Isomorphism classes of elliptic and hyperelliptic curves over finite fields

We give the number and representatives of isomorphism classes of hyperelliptic curves of genus g defined over finite fields , g=1,2,3. These results have applications to hyperelliptic curve cryptography.     

Special values of elliptic functions at points of the divisors of Jacobi forms

The main result of the paper gives an explicit formula for the sum of the values of even order derivatives with respect to of the Weierstrass -function for the lattice (where is in the upper half-plane) extended over the points in the divisor of (where is a meromorphic Jacobi form) in terms of the coefficients of the Laurent expansion of around .

     

<Emphasis Type="Italic">p</Emphasis>-Adic limit of the Fourier coefficients of weakly holomorphic modular forms of half integral weight

Serre obtained the p-adic limit of the integral Fourier coefficients of modular forms on SL ₂(ℤ) for p = 2, 3, 5, 7. In this paper, we extend the result of Serre to weakly holomorphic modular forms of half integral weight on Γ₀(4N) for N = 1, 2, 4. The proof is based on linear relations among Fourier coefficients of modular forms of half integral weight. As applications to our main result, we obtain congruences on various modular objects, such as those for Borcherds exponents, for Fourier coefficients of quotients of Eisentein series and for Fourier coefficients of Siegel modular forms on the Maass Space.     

Synthesis of a Novel Fused Thiophene‐thieno[3,2‐b]thiophene‐thiophene Donor Monomer and Co‐polymer for Use in OPV and OFETs

The synthesis of a novel fused hexacyclic electron rich monomer incorporating thieno[3,2‐b]thiophene is reported and characterized by single crystal X‐ray diffraction. Suzuki co‐polymerization with benzothiadiazole (BT) afforded a novel low band‐gap polymer P4TBT with high molecular weights and good solution processability. Bulk heterojunction solar cell devices using the P4TBT and [70]PCBM gave power conversion efficiencies of 2.5%. Top‐gate, bottom‐contact field effect transistors (FETs) using P4TBT displayed high hole mobilities of 0.07 cm² · Vs⁻¹ demonstrating the suitability of the novel monomer and polymer for use in high performing organic electronic devices.

     

The heat operator and mock Jacobi forms

We study a necessary and sufficient condition for Jacobi integrals of weight -r+\fracj2-r+\frac{j}{2}, r∈ℤ≥0, and index ℳ^(j) on ℋ×ℂ ^j to have a dual Jacobi form of weight r+\fracj2+2r+\frac{j}{2}+2 and index ℳ^(j). Such a meromorphic Jacobi integral with a dual Jacobi form is called a mock Jacobi form whose concept was first introduced by Zagier in Séminaire Bourbaki, 60éme année, 2006–2007, N° 986. In fact, we show the map L^r+1_M^(j)L^{r+1}_{\mathcal{M}^{(j)}} from the space of mock Jacobi forms to that of Jacobi forms is surjective by constructing the corresponding inverse image via Eichler integral of vector valued modular forms which are coming from the theta decomposition of Jacobi forms. We discuss Lerch sums as a typical example.     

In Situ Separation and Analysis of Lipids by Paper Spray Ionization Mass Spectrometry

Paper spray ionization (PSI) is an extractive ambient ionization technique for mass spectrometry (MS), whereby a triangular paper tip serves as the sampling base and the electrospray tip. During PSI, analytes are extracted and transported to the edge of the paper tip by the applied spraying solvent. Analytes can be purified from a sample matrix and separated from each other by this transportation process. In this study, we investigated and utilized the analyte transportation process of PSI for the in situ separation and analysis of lipid mixtures. We found that differential transport of phosphatidylcholine (PC) and triacylglycerol (TAG), the two most abundant lipid classes in animals, occurred during PSI. We also found that the order in which these lipids moved strongly depended on how the spraying solvent was applied to the paper base. The more polar PC moved faster than the less polar TAG during PSI, when a polar solvent was slowly fed into a paper tip, whereas TAG was transported faster than PC when excess solvent was applied to the tip at once. In addition, we achieved a complete separation and detection of PC and TAG by slowly supplying a nonpolar solvent to a PSI tip.     

Anti-inflammatory Glycocalyx-Mimicking Nanoparticles for Colitis Treatment: Construction and In Vivo Evaluation

Common medications for treating inflammatory bowel disease (IBD) have limited therapeutic efficacy and severe adverse effects. This underscores the urgent need for novel therapeutic approaches that can effectively target inflamed sites in the gastrointestinal tract upon oral administration, exerting potent therapeutic efficacy while minimizing systemic effects. Here, we report the construction and in vivo therapeutic evaluation of a library of anti-inflammatory glycocalyx-mimicking nanoparticles (designated GlyNPs) in a mouse model of IBD. The anti-inflammatory GlyNP library was created by attaching bilirubin (BR) to a library of glycopolymers composed of random combinations of the five most naturally abundant sugars. Direct in vivo screening of 31 BR-attached anti-inflammatory GlyNPs via oral administration into mice with acute colitis led to identification of a candidate GlyNP capable of targeting macrophages in the inflamed colon and effectively alleviating colitis symptoms. These findings suggest that the BR-attached GlyNP library can be used as a platform to identify anti-inflammatory nanomedicines for various inflammatory diseases.     

A remark on the Ikeda lift and local singular series polynomials

We relate a certain number-theoretic function occurring in a linear version of Ikeda's lifting map to local singular series polynomials.

     

Splitting the shadow

We derive formulae for the theta series of the two translates of the even sublattice L₀ of an odd unimodular lattice L that constitute the shadow of L. The proof rests on special evaluations of the Jacobi theta series attached to L and to a certain vector. We produce an analogous theorem for codes. Additionally, we construct non-linear formally self-dual codes and relate them to lattices.