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Algebras for which every module is a Koszul module are classified. A necessary condition for the subcategory of graded modules with linear presentations to be equal to the subcategory of Koszul modules is given. This condition is ...
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Algebras for which every module is a Koszul module are classified. A necessary condition for the subcategory of graded modules with linear presentations to be equal to the subcategory of Koszul modules is given. This condition is also a sufficient condition when the algebra is radical cube zero. Finally, these subcategories are studied when the algebra is a one point extension. [References: 9]
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Let A be a δ-Koszul algebra, and let K~δ(A) and L(A) denote the categories of δ-Koszul modules and modules with linear presentations. Some necessary and sufficient conditions for K~δ(A) = L(A) are given. Set E(A) :=⊕i≥0Ext_A...
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Let A be a δ-Koszul algebra, and let K~δ(A) and L(A) denote the categories of δ-Koszul modules and modules with linear presentations. Some necessary and sufficient conditions for K~δ(A) = L(A) are given. Set E(A) :=⊕i≥0Ext_A~i(A_0,A_0) and B(A) := sup{i ∈ N| Ext_A~i(A_0, A_0) ∩ V ≠ 0}, where V is a minimal graded generating space of E(A). In the present paper, we prove that {B(A)| A is δ - Koszul} = N. Finally, the Koszulity of the graded Hopf Galois extension of δ-Koszul algebras is studied.
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In this paper, the notion of Koszul-like algebra is introduced; this notion generalizes the notion of Koszul algebra and includes some Artin-Schelter regular algebras of global dimension 5 as special examples. Basic properties of ...
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In this paper, the notion of Koszul-like algebra is introduced; this notion generalizes the notion of Koszul algebra and includes some Artin-Schelter regular algebras of global dimension 5 as special examples. Basic properties of Koszul-like modules are discussed. In particular, some necessary and sufficient conditions for ΚL(A) = L(A) are provided, where ΚL(A) and L(A) denote the categories of Koszul-like modules and modules with linear presentations (see [1]-[3], etc.) respectively, and A is a Koszul-like algebra. We construct new Koszul-like algebras from the known ones by the "one-point extension." Some criteria for a graded algebra to be Koszul-like are provided. Finally, we construct many classical Koszul objects from the given Koszul-like objects.
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This paper describes a novel alternating and outphasing modulator for the generation and amplification of a linear modulation signal. The architecture requires a linear modulation signal to be represented as two outphasing signals...
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This paper describes a novel alternating and outphasing modulator for the generation and amplification of a linear modulation signal. The architecture requires a linear modulation signal to be represented as two outphasing signals with a constant envelope, which are alternating or switching at the input of two nonlinear amplifiers to produce a linear modulation signal. A power combiner can be employed to cancel the mixed components due to the switching. This will minimize the requirements of the output filter, and hence, simplified the design. This new modulation architecture is simple, and hence, is suitable for all-digital integration. The measurement results of the wideband code division multiple access signal are presented and compared with a conventional linear amplification with nonlinear components architecture.
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The characteristic frequencies of a linear, shift-invariant multidimensional behavior correspond to its nonzero exponential trajectories. The set of polynomial-exponential trajectories belonging to a fixed characteristic frequency...
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The characteristic frequencies of a linear, shift-invariant multidimensional behavior correspond to its nonzero exponential trajectories. The set of polynomial-exponential trajectories belonging to a fixed characteristic frequency of a behavior is investigated: A test is derived for determining whether this space is finite-dimensional, and if so, a basis is constructed. If it is infinite-dimensional, one considers only the polynomial-exponential trajectories up to a certain degree of the polynomial part, and a characterization is given of the asymptotic growth of the dimensions of these spaces as the degree bound tends to infinity. A dual problem is concerned with linear exact modeling, that is, the construction of the so-called most powerful unfalsified model (MPUM): Given a finite set of polynomial-exponential trajectories, the goal is to construct a behavior that contains the data and as little else as possible.
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An analytical model of a super linear optical modulator with high spurious-free-dynamic-range (SFDR> 130 dB) is presented and analyzed. The linear modulator is referred to as IMPACC which stands for Interferometric Modulator with ...
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An analytical model of a super linear optical modulator with high spurious-free-dynamic-range (SFDR> 130 dB) is presented and analyzed. The linear modulator is referred to as IMPACC which stands for Interferometric Modulator with Phase-modulating And Cavity-modulating Components. The modulator is based on a unique combination of a RF-driven phase-modulator (PM) and a ring resonator (RR) within a Mach-Zehnder interferometer (MZI) configuration. Our analysis shows that our design can achieve SFDR values which are approx20 dB higher than the standard MZI modulator and 3-5 dB from the Ring Assisted Mach-Zehnder Interferometer (RAMZI) modulator. Both PM and RR in the IMPACC are simultaneously driven by a RF signal of the same frequency, but not necessarily the same amplitudes. The analytical model shows that the combination of these two optical elements, with the proper choice of RF-driving and device parameters, can lead to four important and compelling consequences. First, it offers a wholistic and elegant model in which the standard MZI modulator and the RAMZI modulator are just special cases of IMPACC. Second, the model offers an excellent parameter optimization methodology for fast parameter (internal and/or external) selection and performance evaluation. Third, it provides additional degree of control through the introduction of an external control parameter, the RF power split ratio (F). Lastly, it demonstrates one unique feature of IMPACC such as adaptive SFDR characteristics, where manufacturing tolerances in the transmission coefficient (tau) of the RR can be compensated with proper adjustments of the external parameter of the power split ratio (F).
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A new method of spatial linear modulation is presented for the RF signal modulation. The constant envelope and phase modulated signals are transmitted to an antenna array and then combined in space; the linear modulation is realiz...
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A new method of spatial linear modulation is presented for the RF signal modulation. The constant envelope and phase modulated signals are transmitted to an antenna array and then combined in space; the linear modulation is realized at the same time. The concentric antenna pairs are applied to eliminate the mismatch of phase delay among the modulated signals from different antenna pairs. The measurement results of an RF signal around 2.45 GHz modulated by a 3.84 Mbps QPSK signal are presented. The proposed spatial modulator is able to simplify RF transmitter design and achieve highly efficient power transmission.
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For each pair of positive integers n, d, we construct a complex (G') over tilde (n) of modules over the bi-graded polynomial ring (R) over tilde = Z[x(1),...{t(M)}], where M roams over all monomials of degree 2n - 2 in {x(1),..., ...
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For each pair of positive integers n, d, we construct a complex (G') over tilde (n) of modules over the bi-graded polynomial ring (R) over tilde = Z[x(1),...{t(M)}], where M roams over all monomials of degree 2n - 2 in {x(1),..., x(d)}. The complex (G') over tilde (n) has the following universal property. Let P be the polynomial ring k[x(1),..., x(d)], where k is a field, and let I-n([d]) (k) be the set of homogeneous ideals I in P, which are generated by forms of degree n, and for which P/I is an Artinian Gorenstein algebra with a linear resolution. If I is an ideal from I-n([d]) (k), then there exists a homomorphism (R) over tilde -> P, so that P circle times ((R) over tilde) (G') over tilde (n) is a minimal homogeneous resolution of PII by free P-modules. The construction of (G') over tilde (n) is equivariant and explicit. We give the differentials of (G') over tilde (n) as well as the modules. On the other hand, the homology of (G') over tilde (n) is unknown as are the properties of the modules that comprise (G') over tilde (n). Nonetheless, there is an ideal (I) over tilde of (R) over tilde and an element delta of (R) over tilde so that IR5 is a Gorenstein ideal of (R) over tilde and (G') over tilde (n) is a resolution of (R) over tilde/(IR) over tilde (delta) by projective (R) over tilde (delta)-modules. The complex (G') over tilde (n) is obtained from a less complicated complex (G') over tilde (n) which is built directly, and in a polynomial manner, from the coefficients of a generic Macaulay inverse system Phi. Furthermore, (I) over tilde is the ideal of (R) over tilde determined by The modules of (G) over tilde (n) are Schur and Weyl modules corresponding to hooks.
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Let Gamma denote a distance-regular graph with classical parameters (D, b, alpha, beta) and b not equal 1, alpha = b - 1. The condition on alpha implies that Gamma is formally self-dual. For b = q(2) we use the adjacency matrix an...
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Let Gamma denote a distance-regular graph with classical parameters (D, b, alpha, beta) and b not equal 1, alpha = b - 1. The condition on alpha implies that Gamma is formally self-dual. For b = q(2) we use the adjacency matrix and dual adjacency matrix to obtain an action of the q-tetrahedron algebra boxed times(q) on the standard module of Gamma. We describe four algebra homomorphisms into boxed times(q) from the quantum affine algebra U-q((sl) over cap (2)); using these we pull back the above boxed times(q)-action to obtain four actions of U-q((sl) over cap (2)) on the standard module of Gamma.
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