2‐Chloro‐4,6‐di­methoxy‐1,3,5‐triazine

The mol­ecules of 2‐chloro‐4,6‐di­methoxy‐1,3,5‐triazine, C₅H₆ClN₃O₂, lie on a crystallographic mirror plane. There is a close contact of 3.180 (3) Å between one of the methyl C atoms and the N atom of a neighboring mol­ecule. Differential scanning calorimetry measurements show that methyl rearrangement does not take place in the solid state, despite the close proximity of the methyl group to the N atom.     

Moving waves and spatiotemporal patterns due to weak thermal effects in models of catalytic oxidation

We analyze the behavior of a microkinetic model of a catalytic reaction coupled with weak enthalpy effects to show that under fixed gas-phase concentrations it can produce moving waves with an intrinsic length scale, when the underlying kinetics is oscillatory. The kinetic model incorporates dissociative oxygen adsorption, reactant adsorption and desorption, and surface reaction. Three typical patterns may emerge in a one-dimensional system (a long wire or a ring): homogeneous oscillations, a family of moving waves propagating with constant velocities, and patterns with multiple source/sink points. Pattern selection depends on the ratio of the system length to the intrinsic wave length and the governing parameters. We complement these analysis with simulations that revealed a plethora of patterned states on one- and two-dimensional systems (a disk or a cylinder). This work shows that weak long-range coupling due to high feed rates maintains such patterns, while low feed rates or strong long-range interaction can gradually suppress the emerging patterns.     

Solving the spectroscopic phase: imaging excited wave packets and extracting excited state potentials from fluorescence data

We develop an inversion scheme for obtaining the signs of transition-dipole amplitudes from fluorescence line intensities. Using the amplitudes thus obtained we show how to extract highly accurate excited state potential(s) and the transition-dipole(s) as a function of inter-nuclear displacements. The same dipole amplitudes can also be used to extract the phase and amplitude of unknown time-evolving wave packets, in essentially a quantum non-demolition manner. The procedure, which is demonstrated for the A((1)∑) and B((1)Π(u)) states of the Na(2) molecule, is shown to yield reliable results even when we are given incomplete or uncertain data. We also demonstrate the success of our approach in extracting double minimum potentials. The inversion scheme is in principle applicable to any polyatomic molecule.     

Maximum Conditional Probability Stochastic Controller for Linear Systems with Additive Cauchy Noises

Journal of Optimization Theory and Applications - Motivated by the sliding mode control approach, a stochastic controller design methodology is developed for discrete-time, vector-state linear...     

Reduced limits for nonlinear equations with measures

We consider equations (E) −Δu+g(u)=μ in smooth bounded domains Ω⊂RN, where g is a continuous nondecreasing function and μ is a finite measure in Ω. Given a bounded sequence of measures (μk), assume that for each k?1 there exists a solution uk of (E) with datum μk and zero boundary data. We show that if uk→u# in L¹(Ω), then u# is a solution of (E) relative to some finite measure μ#. We call μ# the reduced limit of (μk). This reduced limit has the remarkable property that it does not depend on the boundary data, but only on (μk) and on g. For power nonlinearities g(t)=|t|^q−1t, ∀t∈R, we show that if (μk) is nonnegative and bounded in W−2,q(Ω), then μ and μ# are absolutely continuous with respect to each other; we then produce an example where μ#≠μ.     

Inclusion relations involving k-numerical ranges

Let W_k(A) denote the k-numerical range of an n × n matrix A. It is known that W_i(A) ? W_j(A) for 1 ? j? i? n. It this paper we derive more general inclusion relations of the form Σⁿ_iλ_iW_i(A) ? Σⁿ_iμ_iW_i(A), where λ_i, μ_i are real coefficients.     

Production of radially or azimuthally polarized beams in solid-state lasers and the elimination of thermally induced birefringence effects

Production and amplification of radially and azimuthally (tangentially) polarized laser beams are demonstrated. Based on the different focusing between radially and tangentially polarized light in thermally stressed isotropic laser rods, Nd:YAG laser oscillators were developed to produce low-loss stable oscillation in a single polarization. Pure radially polarized light at 70 W with M2 = 2 and on-axis impure radially polarized light at 150 W with M2 = 2.5 were achieved. The radially polarized beams were then amplified while good beam quality and polarization purity were retained. Complete elimination of thermal-birefringence-induced aberrations was demonstrated. This should allow much better beam quality from rod-based high-power lasers.     

A problem on conjugacy of matrices

Let F be an infinite field and n?12. Then the number of conjugacy classes of the upper triangular nilpotent matrices in M_n(F) under action by the subgroup of GL_n(F) consisting of all the upper triangular matrices is infinite.