Dimension 2m Research Articles

Existence of extrinsic polyharmonic maps in critical dimensions

Given two closed Riemannian manifolds M of dimension 2m and N⊂RK, we study the existence problem of extrinsic m-polyharmonic maps in a fixed free homotopy class from M to N. We prove that any energy-minimizing sequence in a fixed free homotopy class subsequently converges locally in Wm,2 to a smooth extrinsic m-polyharmonic map except possibly at most finitely many energy concentration points. Moreover, at an energy concentration point we show that there exists a non-constant smooth extrinsic m-polyharmonic map from R2m to N by blow-up analysis. As a consequence, when the homotopy group π2m(N) is trivial, we prove that there always exists a minimizing extrinsic m-polyharmonic map in every free homotopy class in [M2m,N]. This generalizes the celebrated existence results for harmonic maps (m=1) and biharmonic maps (m=2). The main technical ingredient is an ϵ-regularity for an energy-minimizing sequence, which is new for m-polyharmonic maps and should be of independent interest.

On the relation between cosymplectic and symplectic structures

In this paper we study some aspects of the relationship between cosymplectic and symplectic structures. In particular, we show that similar to the symplectic case, one can prove a nonsqueezing theorem for cosymplectomorphisms on R2m+1. Using this nonsqueezing theorem, we can define the concept of “cosymplectic capacity”. We show that the set of all cosymplectic capacities on cosymplectic manifolds of dimension 2m+1 has a close relationship with the set of all symplectic capacities on symplectic manifolds of dimension 2m. Furthermore, we study the relationship between fixed points of cosymplectomorphisms and symplectomorphisms.

Flow-modulated comprehensive two-dimensional gas chromatography combined with time-of-flight mass spectrometry: use of hydrogen as a more sustainable alternative to helium.

The present research is focused on the use and evaluation of hydrogen, as a more sustainable alternative to helium, within the context of fast flow modulation comprehensive two-dimensional gas chromatography-time-of-flight mass spectrometry. In such a respect, a comparison was made between the two mobile phases in terms of speed and overall chromatography performance. All experiments were carried out by using the following column set: low polarity with dimensions 10m × 0.25mm ID × 0.25µm df and medium polarity with dimensions 2m × 0.10mm ID × 0.10µm df. Fundamental gas chromatography parameters (efficiency, resolution) were measured under different experimental conditions, using the two carrier gases. Efficiency was measured in both the first and second dimensions, using a probe compound under isothermal conditions; after defining the optimum carrier gas conditions, a mixture containing 20 pesticides was analyzed to measure resolution, again in the first and second dimensions, using a temperature program. It was found (as expected) that a similar chromatography performance could be attained when using hydrogen, albeit with a circa 25% reduction in analysis time. Signal-to-noise ratios of the pesticides were calculated, using both carrier gases, with such values generally reduced (on average by 14%) when using hydrogen. Finally, a comparison was made between mass spectral profiles obtained analyzing the pesticides and fatty acid methyl esters using the two mobile phases. Even though mass spectral differences were observed, the ion profiles could be considered generally similar.

Real Hypersurfaces in Complex Grassmannians of Rank Two

It is known that there does not exist any Hopf hypersurface in complex Grassmannians of rank two of complex dimension 2m with constant sectional curvature for m≥3. The purpose of this article is to extend the above result, and without the Hopf condition, we prove that there does not exist any locally conformally flat real hypersurface for m≥3.

Conservation laws for even order elliptic systems in the critical dimension - a new approach

We consider elliptic systems of order 2m in dimension 2m which are generalizations of extrinsic and intrinsic polyharmonic maps. We show the existence of a conservation law for these systems by using a small perturbation of Uhlenbeck’s gauge fixing matrix.

Improved Adams-type inequalities and their extremals in dimension 2m

In this paper, we prove the existence of an extremal function for the Adams–Moser–Trudinger inequality on the Sobolev space [Formula: see text], where [Formula: see text] is any bounded, smooth, open subset of [Formula: see text], [Formula: see text]. Moreover, we extend this result to improved versions of Adams’ inequality of Adimurthi-Druet type. Our strategy is based on blow-up analysis for sequences of subcritical extremals and introduces several new techniques and constructions. The most important one is a new procedure for obtaining capacity-type estimates on annular regions.

Uniqueness and stability of the saddle-shaped solution to the fractional Allen–Cahn equation

In this paper we prove the uniqueness of the saddle-shaped solution u\colon \mathbb{R}^{2m} \to \mathbb{R} to the semilinear nonlocal elliptic equation (-\Delta)^\gamma u = f(u) in \mathbb{R}^{2m} , where \gamma \in (0,1) and f is of Allen–Cahn type. Moreover, we prove that this solution is stable if 2m\geq 14 . As a consequence of this result and the connection of the problem with nonlocal minimal surfaces, we show that the Simons cone \{(x', x'') \in \mathbb{R}^{m}\times \mathbb{R}^m: |x'| = |x''|\} is a stable nonlocal (2\gamma) -minimal surface in dimensions 2m\geq 14 . Saddle-shaped solutions of the fractional Allen–Cahn equation are doubly radial, odd with respect to the Simons cone, and vanish only in this set. It was known that these solutions exist in all even dimensions and are unstable in dimensions 2, 4, and 6. Thus, after our result, the stability remains an open problem only in dimensions 8, 10, and 12. The importance of studying this type of solution is due to its relation with the fractional version of a conjecture by De Giorgi. Saddle-shaped solutions are the simplest non 1D candidates to be global minimizers in high dimensions, a property not yet established in any dimension.

Prediction of Heat Transfer Coefficient and Pressure Drop in Wire Heat Exchanger Working with R-134a and R-600a

An experimental and theoretical works were carried out to model the wire condenser in the domestic refrigerator by calculating the heat transfer coefficient and pressure drop and finding the optimum performance. The two methods were used for calculation, zone method, and an integral method. The work was conducted by using two wire condensers with equal length but different in tube diameters, two refrigerants, R-134a and R-600a, and two different compressors matching the refrigerant type. In the experimental work, the optimum charge was found for the refrigerator according to ASHRAE recommendation. Then, the tests were done at 32˚C ambient temperature in a closed room with dimension (2m*2m*3m). The results showed that the average heat transfer coefficient for the R-600a was higher than the R-134a, so the length of the wire tube was longer with R-134a than R-600a. The pressure drop for the smaller tube diameter was higher than the other tube. The second law thermodynamic efficiency was higher for R-600a, which reached 41%. The entropy generation minimization analysis showed that the R-600a refrigerant type and smaller tube diameter are approached the optimum point.

Von Neumann dimension, Hodge index theorem and geometric applications

A reformulation of the Hodge index theorem within the framework of Atiyah’s $$L^2$$ -index theory is provided. More precisely, given a compact Kahler manifold (M, h) of even complex dimension 2m, we prove that $$\begin{aligned} \sigma (M)=\!\!\sum _{p,q=0}^{2m}\!(-1)^ph_{(2),\Gamma }^{p,q}(M) \end{aligned}$$ where $$\sigma (M)$$ is the signature of M and $$h_{(2),\Gamma }^{p,q}(M)$$ are the $$L^2$$ -Hodge numbers of M with respect to a Galois covering having $$\Gamma $$ as group of deck transformations. Likewise we also prove an $$L^2$$ -version of the Frolicher index theorem, see (3). Afterwards we give some applications of these two theorems and finally we conclude this paper by collecting other properties of the $$L^2$$ -Hodge numbers.

Mechanical behavior of the reinforced concrete frame with masonry filling Comportement mécanique des portiques en béton armé avec remplissage en maçonnerie

Masonry is often used in the most of reinforced concrete structure constructions as a filling material that is important on structural characteristics. Structural contribution in the calculations was neglected or misunderstood, mainly due to the lack of a practical calculation methods and an appropriate regulatory tool.The analysis of frames filled with masonry is very complex. This complexity is linked from one part to the difference in the nature of elements and its behavior that make up the masonry itself (brick and mortar) and their interaction, and on the other part, for the large dispersion that characterizes the bricks as well as the execution's quality parameters which make it difficult to define reliable criteria for the masonry. The objective of this work is to experimentally highlight the influence of the hollow brick masonry filler, commonly used in Morocco, on reinforced concrete frames subject to lateral stresses, to deepen understanding the seismic behavior of the masonry structures by evaluating the structural performance of a specimen wall. These experimental results will be compared to those found by modeling prototypes, using SAP 2000 software, based on various approaches and models as well as other results deduced from the other researchers. The experimental study was carried out according to standard NF EN 1052-3 on two reinforced concrete frames, of dimensions (2m X 1.6m), the one with the masonry filling, and the other without filling in order to determine the initial characteristic resistance to the shearing of the masonry walls. The obtained results showed that a filling has a beneficial effect on rigidity which can be doubled compared to an empty frame. in the same way the lateral resistance. But this effect is much contrasted; it depends a lot on the characteristics essentially of the materials (bricks and concrete). This is the main reason, which justifies the divergence of the results deduced from the nine models that we used.

Injectivity of Generalized Wronski Maps

AbstractWe study linear projections on Plücker space whose restriction to the Grassmannian is a non-trivial branched cover. When an automorphism of the Grassmannian preserves the fibers, we show that the Grassmannian is necessarily of m-dimensional linear subspaces in a symplectic vector space of dimension 2m, and the linear map is the Lagrangian involution. The Wronski map for a self-adjoint linear diòerential operator and the pole placement map for symmetric linear systems are natural examples.

Constructing (0,1)-matrices with large minimal defining sets

If D is a partially filled-in (0,1)-matrix with a unique completion to a (0,1)-matrix M (with prescribed row and column sums), we say that D is a defining set for M. Let A2m,m be the set of (0,1)-matrices of dimensions 2m×2m with uniform row and column sum m. It is shown in Cavenagh (2013) [3] that the smallest possible size for a defining set of an element of A2m,m is precisely m2. In this note when m is a power of two we construct an element of A2m,m which has no defining set of size less than 2m2−o(m2). Given that it is easy to show any A2m,m has a defining set of size at most 2m2, this construction is asymptotically optimal. Our construction is based on a array, defined using linear algebra, in which any subarray has asymptotically the same number of 0's and 1's.

C1-Genericity of symplectic diffeomorphisms and lower bounds for topological entropy

ABSTRACTThere is a C1-residual (Baire second class) subset of symplectic diffeomorphisms on 2d-dimensional manifold, d ≥ 1, such that for every non-Anosov f in , its topological entropy is lower bounded by the supremum of the Lyapunov exponents of their hyperbolic periodic points in the unbreakable central sub-bundle (i.e. central direction with no dominated splitting) of f. The previous result deals with the fact that for f in a C1-residual set of symplectic diffeomorphisms (containing ) satisfies a trichotomy: or f is Anosov or f is robustly transitive partially hyperbolic with unbreakable centre of dimension 2m, 0 < m < d, or f has totally elliptic periodic points dense on M. In the second case, we also show the existence of a sequence of m-elliptic periodic points converging to M. Indeed, contains an C1 open and dense subset of symplectic diffeomorphisms.

Investigation of Affecting Parameters on Heap Leaching Performance and Reducing Acid Consumption of Low Grade Oxide-Sulfide Copper Ore

Heap leaching method is known as cheap method for copper extraction. Presence of clay and acid consumer waste minerals are the most critical issues because they may bring out the process from economic mode. For reduce acid consumption and increasing copper extraction in heap leaching method, about 3 tons sample was taken randomly from different low grade zones. After homogenization and spelling into small parts, bottle roll tests were carried out to achieve maximum copper recovery and acid consumption in a short time at pH= 1, 1.1 and 1.2. Maximum copper recovery were 60.8, 60.2 and 60.1%, respectively. Also acid consumption were 107.30, 99.90 and 93.23 kg/t of ore, respectively. After diagnostic tests, nine columns with dimension 2m height and 15cm diameter were filled by 0.5, 1 and 1.5 inches ore. Columns were irrigated with 7, 9 and 11 g/l as acid solution concentration at flow rates of 7, 11 and 15 l/m2*h for 63 days. Results showed that there are high correlation between copper and iron recoveries. Copper recovery changed from 25.5% to 58.9% while iron recovery changed from 4.7% to 15.2%. Acid consumption were achieved between 18 to 54 kg per ton of ore. Acid solution concentration and irrigation flow rate are the most important parameters on the copper and iron recoveries. By increasing of leaching period Copper extraction will increase, but acid will be waste more. Copper and iron recoveries were increased with increasing the acid solution concentration and irrigation flow rate but Increasing in amount of acid consumption does not increase copper extraction inevitably. Irrigation flow rate of acid solution has significant effect on acid consumption. With decreasing the ore particle size, both of copper recovery and acid consumption were increased.

Design and analysis of codes with distance 4 and 6 minimizing the probability of decoder error

The problem of minimization of the decoder error probability is considered for shortened codes of dimension 2m with distance 4 and 6. We prove that shortened Panchenko codes with distance 4 achieve the minimal probability of decoder error under special form of shortening. This shows that Hamming codes are not the best. In the paper, the rules for shortening Panchenko codes are defined and a combinatorial method to minimize the number of words of weight 4 and 5 is developed. There are obtained exact lower bounds on the probability of decoder error and the full solution of the problem of minimization of the decoder error probability for [39,32,4] and [72,64,4] codes. For shortened BCH codes with distance 6, upper and lower bounds on the number of minimal weight codewords are derived. There are constructed [45,32,6] and [79,64,6] BCH codes with the number of weight 6 codewords close to the lower bound and the decoder error probabilities are calculated for these codes. The results are intended for use in memory devices.

Existence of saddle solutions of a nonlinear elliptic equation involving p-Laplacian in more even-dimensional spaces

We show that there exist saddle solutions of the nonlinear elliptic equation involving the p-Laplacian, p > 2, -Δpu = f(u) in R2m for all dimensions satisfying 2m ≥ p, by using sub-supersolution method. The existence of saddle solutions of the above problem was known only in dimensions 2m ≥ 2p.

On Semisimple Hopf Algebras of Dimension 2 m , II

In this paper we classify, up to equivalence, all semisimple nontrivial Hopf algebras of dimension 22n+1 for n ≥ 2 over an algebraically closed field of characteristic 0 with the group of group-like elements isomorphic to \(\mathbb {Z}_{2^{n}}\times \mathbb {Z}_{2^{n}}\). Moreover we classify all such nonisomorphic Hopf algebras of dimension 32 and show that they are not twist-equivalent to each other. More generally, given an abelian group of order 2m−1 we give an upper bound for the number of nonisomorphic nontrivial Hopf algebras of dimension 2m which have this group as their group of group-like elements.

A Gross–Kohnen–Zagier type theorem for higher-codimensional Heegner cycles

We prove that Heegner cycles of codimension m+1 inside Kuga-Sato type varieties of dimension 2m+1 are coefficients of modular forms of weight 3/2+m in the appropriate quotient group. The main technical tool for generating the necessary relations is a Borcherds style theta lift with polynomials. We also show how this lift defines a new singular Shimura-type correspondence from weakly holomorphic modular forms of weight 1/2-m to meromorphic modular forms of weight 2m+2.

Yang–Mills solutions and dyons on cylinders over coset spaces with Sasakian structure

We present solutions of the Yang–Mills equation on cylinders R×G/H over coset spaces of odd dimension 2m+1 with Sasakian structure. The gauge potential is assumed to be SU(m)-equivariant, parameterized by two real, scalar-valued functions. Yang–Mills theory with torsion in this setup reduces to the Newtonian mechanics of a point particle moving in R2 under the influence of an inverted potential. We analyze the critical points of this potential and present an analytic as well as several numerical finite-action solutions. Apart from the Yang–Mills solutions that constitute SU(m)-equivariant instanton configurations, we construct periodic sphaleron solutions on S1×G/H and dyon solutions on iR×G/H.

Characterisation of glass electrodes and RPC detectors for INO-ICAL experiment

India-based Neutrino Observatory (INO) is a planned neutrino experiment to be build up in southern part of India.The INO observatory will host a 51 kton Iron Calorimeter (ICAL) detector to detect atmospheric neutrinos. Resistive Plate Chamber (RPC) has been chosen as the active detector element for the ICAL experiment. The ICAL experiment will consist of about 28,000 RPC's of dimension 2m × 2m, divided into three modules. The experiment is planned to take data at least for 20 years from its start date. Due to the large number of RPC needed for ICAL experiment and the long lifetime of the experiment, it is necessary to carry out detailed R&D to optimise each and every parameter of the detector performance. We report on the performance studies carried out on the RPC's made with these electrodes, and finally compare the detector performance with that of the material properties to optimise the detector parameters.