## Journals

- Advances in Mathematics of Communications
- Big Data & Information Analytics
- Communications on Pure & Applied Analysis
- Discrete & Continuous Dynamical Systems - A
- Discrete & Continuous Dynamical Systems - B
- Discrete & Continuous Dynamical Systems - S
- Evolution Equations & Control Theory
- Inverse Problems & Imaging
- Journal of Computational Dynamics
- Journal of Dynamics & Games
- Journal of Geometric Mechanics
- Journal of Industrial & Management Optimization
- Journal of Modern Dynamics
- Kinetic & Related Models
- Mathematical Biosciences & Engineering
- Mathematical Control & Related Fields
- Mathematical Foundations of Computing
- Networks & Heterogeneous Media
- Numerical Algebra, Control & Optimization
- AIMS Mathematics
- Conference Publications
- Electronic Research Announcements
- Mathematics in Engineering

### Open Access Journals

JIMO

In this paper we extend the standard LIBOR market model to
accommodate the pronounced phenomenon of implied volatility smiles/skews.
We adopt a multiplicative stochastic factor to the volatility functions of all
relevant forward rates. The stochastic factor follows a square-root diffusion
process, and it can be correlated to the forward rates. For any swap rate, we
derive an approximate process under its corresponding forward swap measure.
By utilizing the analytical tractability of the approximate process, we develop
a closed-form formula for swaptions in term of Fourier transforms. Extensive
numerical tests are carried out to support the swaptions formula. The extended
model captures the downward volatility skews by taking negative correlations
between forward rates and their volatilities, which is consistent with empirical
findings.

MBE

In this paper, we consider the population growth of a single species
living in a two-dimensional spatial domain. New reaction-diffusion
equation models with delayed nonlocal reaction are developed in
two-dimensional bounded domains combining different boundary conditions.
The important feature of the models is the reflection of the joint
effect of the diffusion dynamics and the nonlocal maturation delayed effect.
We consider and analyze numerical solutions of the mature population
dynamics with some well-known birth functions. In particular,
we observe and study the occurrences of asymptotically stable
steady state solutions
and periodic waves for the two-dimensional problems with
nonlocal delayed reaction. We also investigate numerically the
effects of various parameters on the period, the peak and the shape of
the periodic wave as well as the shape of the asymptotically
stable steady state solution.

keywords:
time delay
,
numerical analysis.
,
2-d reaction-diffusion
,
non-local reac-
tion
,
population growth

JIMO

We claim a conclusion on Multi-Dimensional
Knapsack Problem (MKP), which extends an important proposition by
Dantzig firstly, then address to a special case of this problem,
and constitute a polynomial algorithm, extending Zukerman et al's
work.

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