Let X be the Shimura curve corresponding to the quaternion algebra over Q ramified only at 3 and ... more Let X be the Shimura curve corresponding to the quaternion algebra over Q ramified only at 3 and 13. B. Jordan showed that X Q( √ −13) is a counterexample to the Hasse principle. Using an equation of X found by A. Kurihara, it is shown here, by elementary means, that X has no Q( √ −13)-rational divisor classes of odd degree. A corollary of this is the fact that this counterexample is explained by the Manin obstruction.
Let P and E be two n X n complex matrices such that for sufficiently small positive e, P + eE is ... more Let P and E be two n X n complex matrices such that for sufficiently small positive e, P + eE is nonnegative and irreducible. It is known that the spectral radius of P + e E and corresponding (normalized) eigenvector have fractional power series expansions. The goal of the paper is to develop an algorithm for computing the coefficients of these expansions under two (restrictive) assumptions, namely that P has a Single Jordan block corresponding to its spectral radius and that the (unique up to scalar multiples) left and right eigenvectors of P corresponding to its spectral
IEEE Transactions on Wireless Communications, 2008
ABSTRACT In this paper, we present a model for wireless losses in packet transmission data networ... more ABSTRACT In this paper, we present a model for wireless losses in packet transmission data networks. The model provides information about the wireless channel status that can be used in congestion control schemes. A Finite State Markov Channel (FSMC) approach is implemented to model the wireless slow fading for different modulation schemes. The arrival process statistics of the packet traces determine the channel state transition probabilities, where the statistics of both error-free and erroneous bursts are captured. Later, we establish SNR partitioning scheme that uses the transition probabilities as a basis for the state margins. The crossover probability associated with each state is calculated accordingly. We also propose an end-to-end approach to loss discrimination based on the channel state estimation at the receiver. Finally, we present a scheme for finding the channel optimal number of states as a function of the SNR. The presented FSMC approach does not restrict the state transitions to the adjacent states, nor does impose constant state duration as compared to some literature studies. We validate our model by experimental packet traces. Our simulation results show the feasibility of building a fading channel model for better wireless-loss awareness.
We study finite-dimensional representations of quantum affine algebras using q-characters. We pro... more We study finite-dimensional representations of quantum affine algebras using q-characters. We prove the conjectures from [FR] and derive some of their corollaries. In particular, we prove that the tensor product of fundamental representations is reducible if and only if at least one of the pairwise normalized R-matrices has a pole.
A nonpolycyclic nilpotent-by-cyclic group Γ can be expressed as the HNN extension of a finitely-g... more A nonpolycyclic nilpotent-by-cyclic group Γ can be expressed as the HNN extension of a finitely-generated nilpotent group N . The first main result is that quasi-isometric nilpotent-by-cyclic groups are HNN extensions of quasi-isometric nilpotent groups. The nonsurjective injection defining such an extension induces an injective endomorphism φ of the Lie algebra g associated to the Lie group in which N is a lattice. A normal form for automorphisms of nilpotent Lie algebras-permuted absolute Jordan form-is defined and conjectured to be a quasi-isometry invariant. We show that if φ, θ are endomorphisms of lattices in a fixed Carnot group G, and if the induced automorphisms of g have the same permuted absolute Jordan form, then Γ φ , Γ θ are quasi-isometric. Two quasi-isometry invariants are also found:
Here is discussed application of the Weyl pair to construction of universal set of quantum gates ... more Here is discussed application of the Weyl pair to construction of universal set of quantum gates for high-dimensional quantum system. An application of Lie algebras (Hamiltonians) for construction of universal gates is revisited first. It is shown next, how for quantum computation with qubits can be used two-dimensional analog of this Cayley-Weyl matrix algebras, i.e. Clifford algebras, and discussed well known applications to product operator formalism in NMR, Jordan-Wigner construction in fermionic quantum computations. It is introduced universal set of quantum gates for higher dimensional system (``qudit''), as some generalization of these models. Finally it is briefly mentioned possible application of such algebraic methods to design of quantum processors (programmable gates arrays) and discussed generalization to quantum computation with continuous variables.
Let X be the Shimura curve corresponding to the quaternion algebra over Q ramified only at 3 and ... more Let X be the Shimura curve corresponding to the quaternion algebra over Q ramified only at 3 and 13. B. Jordan showed that X Q( √ −13) is a counterexample to the Hasse principle. Using an equation of X found by A. Kurihara, it is shown here, by elementary means, that X has no Q( √ −13)-rational divisor classes of odd degree. A corollary of this is the fact that this counterexample is explained by the Manin obstruction.
Let P and E be two n X n complex matrices such that for sufficiently small positive e, P + eE is ... more Let P and E be two n X n complex matrices such that for sufficiently small positive e, P + eE is nonnegative and irreducible. It is known that the spectral radius of P + e E and corresponding (normalized) eigenvector have fractional power series expansions. The goal of the paper is to develop an algorithm for computing the coefficients of these expansions under two (restrictive) assumptions, namely that P has a Single Jordan block corresponding to its spectral radius and that the (unique up to scalar multiples) left and right eigenvectors of P corresponding to its spectral
IEEE Transactions on Wireless Communications, 2008
ABSTRACT In this paper, we present a model for wireless losses in packet transmission data networ... more ABSTRACT In this paper, we present a model for wireless losses in packet transmission data networks. The model provides information about the wireless channel status that can be used in congestion control schemes. A Finite State Markov Channel (FSMC) approach is implemented to model the wireless slow fading for different modulation schemes. The arrival process statistics of the packet traces determine the channel state transition probabilities, where the statistics of both error-free and erroneous bursts are captured. Later, we establish SNR partitioning scheme that uses the transition probabilities as a basis for the state margins. The crossover probability associated with each state is calculated accordingly. We also propose an end-to-end approach to loss discrimination based on the channel state estimation at the receiver. Finally, we present a scheme for finding the channel optimal number of states as a function of the SNR. The presented FSMC approach does not restrict the state transitions to the adjacent states, nor does impose constant state duration as compared to some literature studies. We validate our model by experimental packet traces. Our simulation results show the feasibility of building a fading channel model for better wireless-loss awareness.
We study finite-dimensional representations of quantum affine algebras using q-characters. We pro... more We study finite-dimensional representations of quantum affine algebras using q-characters. We prove the conjectures from [FR] and derive some of their corollaries. In particular, we prove that the tensor product of fundamental representations is reducible if and only if at least one of the pairwise normalized R-matrices has a pole.
A nonpolycyclic nilpotent-by-cyclic group Γ can be expressed as the HNN extension of a finitely-g... more A nonpolycyclic nilpotent-by-cyclic group Γ can be expressed as the HNN extension of a finitely-generated nilpotent group N . The first main result is that quasi-isometric nilpotent-by-cyclic groups are HNN extensions of quasi-isometric nilpotent groups. The nonsurjective injection defining such an extension induces an injective endomorphism φ of the Lie algebra g associated to the Lie group in which N is a lattice. A normal form for automorphisms of nilpotent Lie algebras-permuted absolute Jordan form-is defined and conjectured to be a quasi-isometry invariant. We show that if φ, θ are endomorphisms of lattices in a fixed Carnot group G, and if the induced automorphisms of g have the same permuted absolute Jordan form, then Γ φ , Γ θ are quasi-isometric. Two quasi-isometry invariants are also found:
Here is discussed application of the Weyl pair to construction of universal set of quantum gates ... more Here is discussed application of the Weyl pair to construction of universal set of quantum gates for high-dimensional quantum system. An application of Lie algebras (Hamiltonians) for construction of universal gates is revisited first. It is shown next, how for quantum computation with qubits can be used two-dimensional analog of this Cayley-Weyl matrix algebras, i.e. Clifford algebras, and discussed well known applications to product operator formalism in NMR, Jordan-Wigner construction in fermionic quantum computations. It is introduced universal set of quantum gates for higher dimensional system (``qudit''), as some generalization of these models. Finally it is briefly mentioned possible application of such algebraic methods to design of quantum processors (programmable gates arrays) and discussed generalization to quantum computation with continuous variables.
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Papers by Jordan Ek