We obtain effective asymptotics for the coefficients of q-expansions which involve partial theta functions. As applications, we obtain effective asymptotics for ranks, and cranks of integer partitions. Moreover, from these effective estimates, we obtain asymptotic inequalities among them with effective lower bounds.

In this paper, we give relationship between Bernoulli-Euler polynomials and convolution sums of divisor functions. First, we establish two explicit formulas for certain combinatoric convolution sums of divisor functions derived from Bernoulli and Euler polynomials. Second, as applications, we show five identities concerning the third and fourth-order convolution sums of divisor functions expressed by their divisor functions and linear combination of Bernoulli or Euler polynomials.

Certificateless cryptography eliminates the need of certificates in the Public Key Infrastructure and solves the inherent key escrow problem in the ID-based cryptography. In this paper, we point out security pitfalls on the restrictions of an adversary’s final output in security models of certificateless signature schemes by demonstrating key replacement attacks on three certificateless signature schemes in the different security models.

Ring signature is a group-oriented signature with privacy concerns: any verifier can be convinced that the message has been signed by one of the members in the group, but the actual signer remains unknown. Several ring signature schemes based on bilinear pairings have been proposed. However, computational complexity for pairing computations of these ring signature schemes grows linearly with the size of the ring. In this paper, we propose an efficient ring signature with constant pairing computations and give its exact security proofs in the random oracle model under the Computational co-Diffie–Hellman assumption. We then investigate the performance of our scheme by choosing the Optimal- Ate pairing on the BN curve defined over a prime field at a 128-bit security level.

Subterranean termites live underground and build tunnel networks to obtain food and nesting space. Afterobtaining food, termites return to their nests to transfer it. The efficiency of termite ment throughthe tunnels is directly connected to their survival. Tunnels should therefore be optimized to ensure highlyefficient returns. An optimization factor that strongly affects ment efficiency is tunnel curvature.In the present study, we investigated traveling behavior in tunnels with different curvatures. We thencharacterized traveling behavior at the level of the individual using hidden Markov models (HMMs)constructed from the experimental data. To observe traveling behavior, we designed 5-cm long artificialtunnels that had different curvatures. The tunnels had widths (W) of 2, 3, or 4 mm, and the linear distancesbetween the two ends of the tunnels were (D) 20, 30, 40, or 50 mm. High values of D indicate low curvature.We systematically observed the traveling behavior of Coptotermes formosanus shiraki and Reticulitermessperatus kyushuensis and measured the time () required for a termite to pass through the tunnel. UsingHMM models, we calculated  for different tunnels and compared the results with the  of real termites.We characterized the traveling behavior in terms of transition probability matrices (TPM) and emissionprobability matrices (EPM) of HMMs. We briefly discussed the construction of a sinusoidal-like tunnelsin relation to the energy required for termites to pass through tunnels and provided suggestions for thedevelopment of more sophisticated HMMs to better understand termite foraging behavior.

We construct quasitoric manifolds of dimension 6 and higher which are not equivariantly homeomorphic to any toric origami manifold. All necessary topological definitions and combinatorial constructions are given and the statement is reformulated in discrete geometrical terms. The problem reduces to existence of planar triangulations with certain coloring and metric properties.

In order to describe the dynamics of crowded ions (charged particles), we use an energetic variational approach to derive a modified Poisson–Nernst–Planck (PNP) system which includes an extra dissipation due to the effective velocity differences between ion species. Such a system has more complicated nonlinearities than the original PNP system but with the same equilibrium states. Using Galerkin's method and Schauder's fixed-point theorem, we develop a local existence theorem of classical solutions for the modified PNP system. Different dynamics (but same equilibrium states) between the original and modified PNP systems can be represented by numerical simulations using finite element method techniques.

We develop Ladyzhenskaya-Prodi-Serrin type spectral regularity criteria for 3D incompressible Navier-Stokes equations in a torus. Concretely, for any $N > 0, let wN$ be the sum of all spectral components of the velocity fields whose wave numbers $|ki| > N for all i = 1, 2, 3$. Then, we show that for any $N > 0$, the finiteness of the Serrin type norm of $wN$ implies the regularity of the flow. It implies that if the flow breaks down in a finite time, the energy of the velocity fields cascades down to the arbitrarily large spectral components of $wN$ and corresponding energy spectrum, in some sense, roughly decays slower than $κ−2$

This study analyzes the well-known MUltiple SIgnal Classification (MUSIC) algorithm to identify unknown support of thin penetrable electromagnetic inhomogeneity from scattered field data collected within the so-called multi-static response matrix in limited-view inverse scattering problems. The mathematical theories of MUSIC are partially discovered, e.g., in the full-view problem, for an unknown target of dielectric contrast or a perfectly conducting crack with the Dirichlet boundary condition (Transverse Magnetic–TM polarization) and so on. Hence, we perform further research to analyze the MUSIC-type imaging functional and to certify some well-known but theoretically unexplained phenomena. For this purpose, we establish a relationship between the MUSIC imaging functional and an infinite series of Bessel functions of integer order of the first kind. This relationship is based on the rigorous asymptotic expansion formula in the existence of a thin inhomogeneity with a smooth supporting curve. Various results of numerical simulation are presented in order to support the identified structure of MUSIC. Although a priori information of the target is needed, we suggest a least condition of range of incident and observation directions to apply MUSIC in the limited-view problem.

Vortex flow imaging is a relatively new medical imaging method for the dynamic visualization of intracardiac blood flow, a potentially useful index of cardiac dysfunction. A reconstruction method is proposed here to quantify the distribution of blood flow velocity fields inside the left ventricle from color flow images compiled from ultrasound measurements. In this paper, a 2D incompressible Navier-Stokes equation with a mass source term is proposed to utilize the measurable color flow ultrasound data in a plane along with the moving boundary condition. The proposed model reflects out-of-plane blood flows on the imaging plane through the mass source term. The boundary conditions to solve the system of equations are derived from the dimensions of the ventricle extracted from 2D echocardiography data. The performance of the proposed method is evaluated numerically using synthetic flow data acquired from simulating left ventricle flows. The numerical simulations show the feasibility and potential usefulness of the proposed method of reconstructing the intracardiac flow fields. Of particular note is the finding that the mass source term in the proposed model improves the reconstruction performance.