metric, with N even, is obtained when one realizes that the first row of table 4.21 already completely describes the spectrum as soon as one lets the parameter k take values in all of Z as opposed to just in N . To see that this is indeed the case, one absorbs the third row into the second row by making the substitution m = k 0 + 1, which affects the multiplicity of the second row only in the case s = N 2 −2 . Next, one shows that when k is allowed to take values in all of Z, one combines the parts of the **spectra** corresponding to s and s 0 , when s + s 0 = N−4 2 if s and s 0 are less than N−4 2 and when s = s 0 = N−2 2 otherwise. As a result we have the following corollary.

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As we mention above, virtual quarks and antiquarks of opposite chirality are attracted to each other due to the strong interactions and destabilize the trivial vacuum state. A condensate is formed, which gives rise to a nonvanishing **spectral** density of **Dirac** operator modes. So, the presence of the chi- ral condensate is a clear fact of the SCHSB. When hypercubic symmetry is broken, like in the BC fermions case, the total momentum of the pair quark-antiquark of opposite chirality is not zero, be- cause the velocities are di ff erent in di ff erent directions. So for the pair creation is required energy. In this way, the absence of hypercubic symmetry prohibits the creation of such pairs, so there is no condensate. Therefore the chiral symmetry is exact. What we can think is that the conditions for having a chiral condensate, can be fulfilled only if the Lorentz symmetry is present. Using this fact, by changing the counteterms c 3 in the BC **action**, we can find the proper values of c 3 which allows us

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The main focus of this thesis is on the methods and tools that can be used to extract the **spectral** information. Applying the pseudodifferential calculus and the heat trace techniques, in addition to computing the newer terms, we prove the rationality of the **spectral** **action** of the Robertson-Walker metrics, which was conjectured by Chamseddine and Connes. In the second part, we define the canonical trace for Connes’ pseudodiffer- ential calculus on the noncommutative torus and use it to compute the curvature of the determinant line bundle for the noncommutative torus. In the last chapter, the Euler- Maclaurin **summation** formula is used to compute the **spectral** **action** of a **Dirac** operator (with torsion) on the Berger spheres S 3 (T).

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Abstract. In previous work we showed that the chiral condensate of one-flavor QCD exhibits a Silver Blaze phenomenon when the quark mass crosses m = 0: the chiral condensate remains constant while the quark mass crosses the spectrum of the **Dirac** operator, which is dense on the imaginary axis. This behavior can be explained in terms of exponentially large cancellations between contributions from the zero modes and from the nonzero modes when the quark mass is negative. In these proceedings we show that a similar Silver Blaze phenomenon takes places for QCD with one flavor and arbitrary θ- angle, and for QCD with two flavors with different quark masses m 1 and m 2 . In the latter

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The **summation** method was proposed simultaneously to the conversion method as an alterna- tive allowing to study the sub-components of the reactor antineutrino energy spectrum. The antineutrino spectrum associated with one of the four fissioning isotopes in a moderated re- actor can be computed as the sum of the contributions of all FP using the full information available per nucleus in the NDB as described in [20]. This method is useful for several reasons. Not only it is the only one that can be adapted to the computation of the antineu- trino emission associated to various reactor designs, but also it allows for the computation of antineutrino **spectra** for which no integral β spectrum has been measured yet taking into account off-equilibrium effects and allowing the use of different energy binnings of interest for reactor neutrino experimental analyses.

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spectrum changing in the left part of the figure from blue circles to red upside triangles. We see that even a small change of φ across the phase transiton (corresponding to the displacement to the “wrong” phase) gives rise to a drastic change of the spectrum: the eigenvalues are shifted to smaller values thus decreasing the gap. It is evident that this change of the spectrum implies a substantial decreasing of the **Dirac** operator determinant thus indicating that the statistical weight of configuration I displaced to the region θ > π/3 is small.

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The electronic **spectra** of the adducts of copper(II) dithiocarbonates with the various nitrogen donor ligands used were recorded in DMF in the range 12500 cm 1 to 40000 cm 1 . Copper (II) being a d 9 ion gives rise to only one free ion term 2 D which has tenfold spin and orbital degeneracy. In this paper, the intense band corresponding to d-d transition as observed in most of the copper (II) complexes is observed in the range 15500-17600 cm -1 . The main absorption band around 16000 cm -1 can be assigned to d XZ, d YZ → d X 2 -Y 2 . A weak shoulder is associated with it due

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In Section , we show that the fundamental equation has a unique solution A(x, t) and the boundary value problem (), () can be uniquely determined from the **spectral** data. In Section , the result is obtained from Lemma that the function S(x, λ) deﬁned by () satisﬁes the equation

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Spectral parameters for Td CoL 2 X2 complexes 18 Spectral parameters for Td thio-complexes 23 Magnetic data for Td CoII complexes 24 Infrared spectra of the ligands 33 Infrared spectra o[r]

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Since 2004, the monolayer graphene has been successfully realized in experiment [1,2]. Subsequently, its intriguing properties originating from the strictly two-dimensional structure and massless **Dirac** fermion-like behavior of low-energy excitation have attracted intensive attention [3,4]. Graphene can be tailored into various edge nanorib- bons. Their semiconducting properties with a tunable band gap dependent on the structural size and geometry make them good candidates for the electric and spintronic devices [5]. Due to this reason, the graphene nanoribbons (GNRs) become of particular interest. According to the edge termination types, the GNRs are generally classified into two basic groups, i.e., the armchair and zigzag GNRs [6-8]. In the tight-binding model with nearest-neighbor approximation, the zigzag GNRs are always metallic and exhibit spin-polarized edge states [6-8]. Instead, the arm- chair GNRs (AGNRs) show metallic characteristics when only M = 3n + 2 (M denotes its width with n ∈ integer), whereas they are semiconducting otherwise [7-9]. Due to

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Also, the operator **action** makes the post-impulse equa- tion homogeneous. All of this makes the process of ob- taining the solution considerably easier. As it has been mentioned before, in the case of Example 1 referring to the metal rod heated impulsively, the term associated with heat conduction disappears from the impulse instant equation. This is reconciled with the physical reality, i.e., there is no time for this process to take place.

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A series of quantum search algorithms have been proposed recently providing an algebraic speedup compared to classical search algorithms from N to p ﬃﬃﬃﬃ N , where N is the number of items in the search space. In particular, devising searches on regular lattices has become popular in extending Grover ’ s original algorithm to spatial searching. Working in a tight-binding setup, it could be demonstrated, theoretically, that a search is possible in the physically relevant dimensions 2 and 3 if the lattice spectrum possesses **Dirac** points. We present here a proof of principle experiment implementing wave search algorithms and directed wave transport in a graphene lattice arrangement. The idea is based on bringing localized search states into resonance with an extended lattice state in an energy region of low **spectral** density — namely, at or near the **Dirac** point. The experiment is implemented using classical waves in a microwave setup containing weakly coupled dielectric resonators placed in a honeycomb arrangement, i.e., artificial graphene. Furthermore, we investigate the scaling behavior experimentally using linear chains.

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This article is organized as follows. In §2.2 we provide background material about the noncommutative two torus, its pseudodifferential calculus, and heat kernel meth- ods. In §2.3 we explain our construction of a vector bundle over the noncommutative two torus using a twisted **spectral** triple with σ-connections and derive the symbols of the operators necessary for the index calculation. In §2.4 we calculate the explicit local terms that give the index. The appendix contains proofs of new rearrangement lemmas, which overcome the new challenges posed in our calculations due to the presence of an idempotent as well as a conformal factor in our calculations in the noncommutative setting.

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As compared to multispectral imagers, a hyperspectral imaging system provides a much greater number of **spectral** channels, which cover the **spectral** range in a contiguous way, and therefore provide much more complete **spectral** information. Basically every individual pixel of a hyperspectral imaging recording carries the information of an entire **spectral** curve, which enables a more efficient target discrimination and further analysis (Grahn and Geladi 2007).Reflectance is the percentage of the light hitting a material that is then reflected by that material (as opposed to being absorbed or transmitted). A reflectance spectrum shows the reflectance of a material measured across a range of wavelengths[4].Some materials will reflect certain wavelengths of light, while other materials will absorb the same wavelengths. These patterns of reflectance and absorption across wavelengths can uniquely identify certain materials. Field and laboratory spectrometers usually measure reflectance at many narrow, closely spaced wavelength bands, so that the resulting **spectra** appear to be continuous curves.

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The low sample surface temperature enhanced the spectral contrast of quartz but had little effect on spectra of rock materials... In general, there was a decrease in spectral contrast wi[r]

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On the basis of analytical and **spectral** data the tentative structure of the complexes of the type [M(EHPQS) 2 ] and [M(EHPQT) 2 ] are proposed to be octahedral in nature. The synthesized Schiff bases, EHPQS/EHPQT acts as uninegative tridentate ligand. The metal ions are coordinated through alcoholic oxygen by deprotonation and azomethine. The remaining coordination of the metal

This paper is devoted to studying a q-analog of the singular **Dirac** problem. First, we investigate some **spectral** properties of the problem. Then we prove the existence of a **spectral** function and establish a Parseval’s equality, for the singular q-**Dirac** system in a Hilbert space. Although there were given some results for this type of problem, we think that Parseval’s equality has not been studied yet.

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Abstract. We investigate convolution semigroups of probabil- ity measures with continuous densities on locally compact abelian groups, which have a discrete subgroup such that the factor group is compact. Two interesting examples of the quotient structure are the d–dimensional torus, and the ad`elic circle. Our main result is to show that the Poisson **summation** formula for the density can be interpreted as a probabilistic trace formula, linking values of the density on the factor group to the trace of the associated semi- group on L 2 -space. The Gaussian is a very important example.

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antineutrinos measured by short baseline experiments was pointed out. This is called the “reactor anomaly”, a new puzzle in the neutrino physics area. Since then, numerous new experimental neutrino projects have emerged. In parallel, computations of the antineutrino **spectra** independant from the ILL data would be desirable. One possibility is the use of the **summation** method, summing all the contributions of the fission product beta decay branches that can be found in nuclear databases. Studies have shown that in order to obtain reliable **summation** antineutrino energy **spectra**, new nuclear physics measurements of selected fission product beta decay properties are required. In these proceedings, we will present the computation methods of reactor antineutrino energy **spectra** and the impact of recent beta decay measurements on **summation** method **spectra**. The link of these nuclear physics studies with short baseline line oscillation search will be drawn and new neutrino physics projects at research reactors will be briefly presented.

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In the present paper, we will consider inverse problems of recovering Q(x), α, β from the given **spectral** and nodal characteristics. In what follows without loss of generality we always assume the mean value of p(x) + q(x) is known a priori. Under this assumption we obtain uniqueness theorems and provide a constructive procedure for the solution. The novelty of this paper lies in the established connections between inverse nodal and **spectral** problems and the use of a set of nodal points of the components y (x, λ n ) of the eigenfunc-

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