Sum Map Research Articles

Recovery from Power Sums

We study the problem of recovering a collection of n numbers from the evaluation of m power sums. This yields a system of polynomial equations, which can be underconstrained (m < n), square (m = n), or overconstrained (m > n). Fibers and images of power sum maps are explored in all three regimes, and in settings that range from complex and projective to real and positive. This involves surprising deviations from the Bézout bound, and the recovery of vectors from length measurements by p-norms.

Summability of the coefficients of a multilinear form

Let T be an m -linear form defined on a product of \ell_p -spaces and let \Lambda\subset\mathbb{N}^m . We investigate the best exponent s such that the sequence of coefficients of T belongs to \ell_s(\Lambda) . The cases \Lambda=\mathbb{N}^m and \Lambda is the diagonal of \mathbb{N}^m are already known. We study the intermediate cases using notions like combinatorial dimension of sets, multiple summing maps and random polynomials.

Broadband white luminescent phosphor Ba(Si7−xAlx)Liy(N10−x+yOx−y):Eu2+ with a high color rendering index for solid state lighting

Broadband white luminescent particles by introducing Li into the crystal structure of Ba(Si7−xAlx)(N10−xOx):Eu2+.

In Operando Synchrotron Studies of NH4+ Preintercalated V2O5·nH2O Nanobelts as the Cathode Material for Aqueous Rechargeable Zinc Batteries.

NH4+ preintercalated V2O5·nH2O nanobelts with a large interlayer distance of 10.9 Å were prepared by the hydrothermal method. The material showed a large specific capacity of 391 mA·h·g-1 at the 500 mA·g-1 current density in aqueous rechargeable zinc batteries. In operando synchrotron X-ray diffraction demonstrated that the material experienced reversible solid-solution reaction and two-phase transition during charge-discharge cycling, accompanied by the reversible formation/decomposition of a ZnSO4Zn3(OH)6·5H2O byproduct. In operando X-ray absorption spectroscopy confirmed the reversible reduction/oxidation of V, together with small changes in the VO6 local structure. The formation of byproduct was attributed to the dehydration of [Zn(H2O)6]2+, which concurrently improved the desolvation of [Zn(H2O)6]2+ into Zn2+. Bond valence sum map analysis and electrochemical impedance spectroscopy demonstrated that the byproduct improved the charge transfer kinetics of the electrode. Cyclic voltammetry and galvanostatic intermittent titration technique showed that the electrode reaction was dominated by ionic intercalation where the discharge capacity in the voltage window of 1.4-0.85 V was attributed to the intercalation of [Zn(H2O)6]2+, followed by the intercalation of Zn2+ at 0.85-0.4 V.

On the Best Proximity Points for p–Cyclic Summing Contractions

We present a condition that guarantees the existence and uniqueness of fixed (or best proximity) points in complete metric space (or uniformly convex Banach spaces) for a wide class of cyclic maps, called p–cyclic summing maps. These results generalize some known results from fixed point theory. We find a priori and a posteriori error estimates of the fixed (or best proximity) point for the Picard iteration associated with the investigated class of maps, provided that the modulus of convexity of the underlying space is of power type. We illustrate the results with some applications and examples.

Structure and Non-Stoichiometry of Double Sodium Molybdates with Scandium and Indium of the Alluaudite Type

The structures and compositions of alluaudite-type double molybdates of sodium with scandium and indium are refined. The formulas Na5R(MoO4)4 (R = Sc, In) have previously been accepted for them, however, our new single crystal X-ray diffraction data show that their compositions noticeably differ from the initial ones: Na5.24Sc0.92(MoO4)4 = Na3.93Sc0.69(MoO4)3 (space group C2/c, Z = 4, a = 12.8911(6) A, b = 13.9149(4) A, c = 7.2544(3) A, α = 113.011(2)°, R = 0.0212) and Na5.74In0.75(MoO4)4 = Na4.31In0.56(MoO4)3 (a = 12.8294(5) A, b = 13.8906(5) A, c = 7.2961(3) A, β = 112.729(1)°, R = 0.0164). This indicates the nonstoichiometry of the studied crystals. Their compositions as well as initial Na5R(MoO4)4 = Na3.75R0.75(MoO4)3 are close to the opposite boundaries of homogeneity regions found near the melting points of double molybdates Na3+3xR1−x(MoO4)3 (R = Sc, In) which are 0.25 ≤ x ≤ 0.35 (R = Sc) and 0.25 ≤ x ≤ 0.45 (R = In). They are consistent with the general formula $$\text{Na}_{9-3x}R_{1+x}^{3+}(\text{MoO}_4)_6$$ that we have previously proposed for alluaudite-type double molybdates of sodium and trivalent metals. The characteristic features of both structures are a partial occupancy of all three crystallographic sites of sodium along with the presence of the mixed octahedral site (Na, R), where R = Sc, In. The features of the crystal structures of the studied compounds, calculations of bond-valence sum maps, and also the previously obtained data of solid-state NMR and non-empirical calculations indicate the predominantly one-dimensional, as in the other alluaudites, character of the sodium ion transport through the chain of Na(3)–Na(3) polyhedra along the c axis. However, at elevated temperatures a two-dimensional conductivity is possible in the (100) plane due to the bridging positions of Na(1) and Na(2).

Rb9–xAg3+xSc2(WO4)9: a new glaserite-related structure type, rubidium disorder, ionic conductivity

A new triple tungstate Rb9-xAg3+xSc2(WO4)9 (0 ≤ x ≤ 0.15) synthesized by solid state reactions and spontaneous crystallization from melts presents a new structure type related to those of Cs7Na5Yb2(MoO4)9 and Na13Sr2Ta2(PO4)9. The title compound in centrosymmetric space group Cmcm contains dimers of two ScO6 octahedra sharing corners with three bridging WO4 tetrahedra. Three pairs of opposite terminal WO4 tetrahedra are additionally linked by AgO2 dumbbells to form {Ag3[Sc2(WO4)9]}9- groups, which together with some rubidium ions are packed in pseudohexagonal glaserite-like layers parallel to (001), but stacking of the layers is different in these three structures. In the title structure, the layers stack with a shift along the b axis and their interlayer space contains disordered Rb+ cations partially substituted by Ag+ ions. Almost linear chains of incompletely filled close Rb3a-Rb3d positions (the shortest distances Rb-Rb are 0.46 to 0.64 Å) are found to locate approximately along the b axis. This positional disorder and the presence of wide common quadrangular faces of Rb2 and Rb3a-Rb3d coordination polyhedra favor two-dimensional ionic conductivity in the (001) plane with Rb+ and Ag+ carriers, which was confirmed with bond valence sum (BVS) maps. Electrical conductivity measurements on Rb9Ag3Sc2(WO4)9 ceramics revealed a first-order superionic phase transition at 570 K with a sharp increase in the electrical conductivity. The conductivity σi= 1.8 × 10-3 S cm-1 at 690 K is comparable with the value of 1.0 × 10-3 S cm-1 (500 K) observed earlier for rubidium-ion transport in pyrochlore-like ferroelectric RbNbWO6.

Aluminum dual doping and oxygen transport pathway in novel Sr11Mo4−xAlxO23 oxide-ion solid electrolytes

Three new electrolytes of composition Sr11Mo4-xAlxO23-δ (x = 0.5, 1.0 and 1.5) were synthesized by wet-chemistry procedures (citrate method) as polycrystalline samples. They were crystallographically studied from synchrotron and neutron diffraction techniques. They derive from the Sr11Mo4O23 complex perovskite, which can be rewritten as Sr1.75□0.25SrMoO5.75, highlighting the relationship with double perovskites A2B′B″O6. From these analyses via Rietveld refinement, a dual doping was found from synchrotron data, where the aluminum is equally allocated at both Sr (B′) and Mo (B″) sites. A detailed analysis of the neutron data from Difference Fourier Maps (DFM) unveiled the oxygen delocalization around the Mo site. From the refined crystal structures at room and high temperatures, a Bond Valence Sum Map (BVSM) analysis was useful to find the oxygen pathway in the crystal structure, and the minimum density to allow connections among oxygen atoms. The structural characterization was complemented with thermogravimetric and thermodilatometric analysis. The ionic conductivity was measured from electrochemical impedance spectroscopy (EIS) in wet and dry air and nitrogen atmospheres.

Synthesis, sintering, electrical properties, and sodium migration pathways of new lyonsite Na 2 Co 2 (MoO 4 )

A new double molybdate Na 2 role=presentation> 2 2 _{2} Co 2 role=presentation> 2 2 _{2} (MoO 4 ) 3 role=presentation> 4 ) 3 4 ) 3 _{4})_{3} was synthesized via solid-state reaction and characterized by single-crystal X-ray diffraction (XRD). This compound is a new member of the lyonsite structure type. It crystallized in the orthorhombic system, space group Pnma with cell parameters a role=presentation> a a a = 5.272(2) Å, b role=presentation> b b b = 10.816(3) Å, and c role=presentation> c c c = 18.064(3) Å. The structure can be described as a three-dimensional framework with hexagonal tunnels in which the Na + role=presentation> + + ^{+} cations lie. The obtained structural model is supported by charge distribution analysis and bond valence sum validation tools. Fourier-transform infrared spectroscopy and scanning electron microscopy analyses were carried out. Ball milling was used to reduce the particle size of the synthesized powder. Dense ceramics with a relative density of 78% were obtained by sintering at 853 K. The conductivity of the title compound was studied for different relative densities. The ionic conductivity at 723 K with an activation energy of 1.2 eV was 3.24 × role=presentation> × × \times 10 − 6 role=presentation> − 6 − 6 ^{-6} S cm − 1 role=presentation> − 1 − 1 ^{-1} . The bond valence sum map model is used to simulate the cation migration pathways in the anionic framework.

No Reference Quality Assessment of Stereo Video Based on Saliency and Sparsity

With the popularity of video technology, stereoscopic video quality assessment (SVQA) has become increasingly important. Existing SVQA methods cannot achieve good performance because the videos’ information is not fully utilized. In this paper, we consider various information in the videos together, construct a simple model to combine and analyze the diverse features, which is based on saliency and sparsity. First, we utilize the 3-D saliency map of sum map, which remains the basic information of stereoscopic video, as a valid tool to evaluate the videos’ quality. Second, we use the sparse representation to decompose the sum map of 3-D saliency into coefficients, then calculate the features based on sparse coefficients to obtain the effective expression of videos’ message. Next, in order to reduce the relevance between the features, we put them into stacked auto-encoder, mapping vectors to higher dimensional space, and adding the sparse restraint, then input them into support vector machine subsequently, and finally, get the quality assessment scores. Within that process, we take the advantage of saliency and sparsity to extract and simplify features. Through the later experiment, we can see the proposed method is fitting well with the subjective scores.

Multi-View Ground-Based Cloud Recognition by Transferring Deep Visual Information

Since cloud images captured from different views possess extreme variations, multi-view ground-based cloud recognition is a very challenging task. In this paper, a study of view shift is presented in this field. We focus both on designing proper feature representation and learning distance metrics from sample pairs. Correspondingly, we propose transfer deep local binary patterns (TDLBP) and weighted metric learning (WML). On one hand, to deal with view shift, like variations of illuminations, locations, resolutions and occlusions, we first utilize cloud images to train a convolutional neural network (CNN), and then extract local features from the part summing maps (PSMs) based on feature maps. Finally, we maximize the occurrences of regions for the final feature representation. On the other hand, the number of cloud images in each category varies greatly, leading to the unbalanced similar pairs. Hence, we propose a weighted strategy for metric learning. We validate the proposed method on three cloud datasets (the MOC_e, IAP_e, and CAMS_e) that are collected by different meteorological organizations in China, and the experimental results show the effectiveness of the proposed method.

Experimental visualization of oxide-ion diffusion paths in pyrochlore-type Yb&lt;sub&gt;2&lt;/sub&gt;Ti&lt;sub&gt;2&lt;/sub&gt;O&lt;sub&gt;7&lt;/sub&gt;

Crystal structure and neutron scattering length density distribution of a pyrochlore-type ytterbium titanate Yb2Ti2O7 have been investigated by in situ neutron powder diffraction measurements at 293 and 1173 K, Rietveld analysis and maximum-entropy method (MEM). In the MEM neutron scattering length density distributions of Yb2Ti2O7, the oxide ion O48f bonding to Ti cation was relatively localized at lower temperature of 293 K, while it was largely distributed at a higher temperature of 1173 K. At 1173 K, one oxide-ion diffusion path along the 〈110〉 unshared edge of TiO6 octahedron was clearly visualized and the other oxide-ion diffusion path along 〈100〉, strictly 〈2 −8x(O48f) + 3 8x(O48f) − 3〉, shared edge of TiO6 octahedron was also indicated. Here x(O48f) is the atomic coordinate x of O48f anion. The MEM neutron scattering length density distribution and difference bond valence sum map at 1173 K strongly suggested that the energy barrier for oxide-ion migration along 〈110〉 directions was lower than that along the 〈100〉 one. Oxide ions three-dimensionally diffuse through both the 〈110〉 and 〈100〉 paths across the unit cell.

Learning local embedding deep features for person re-identification in camera networks

In this paper, we propose a novel feature learning method named local embedding deep features (LEDF) for person re-identification in camera networks. In order to learn the structural information of pedestrian, we first utilize the verification network that does not require explicit identity labels to obtain the local summing maps. We then combine all local summing maps of a pedestrian image to form the holistic summing map which has the same identity label with the original pedestrian image. Finally, we take the holistic summing maps as the input to train the identification network, and then obtain the LEDF from the last fully connected layer. The proposed LEDF fully considers the structural information by learning the local features and meanwhile possesses strong discriminative ability by learning global features. The experimental results on two large-scale datasets (Market-1501 and CUHK03) demonstrate that the proposed LEDF achieves better results than the state-of-the-art methods.

Optical and electrical properties of the yavapaiite-like molybdate NaAl(MoO4)2

Polycrystalline sample of the sodium aluminum molybdate, NaAl(MoO4)2, was prepared by conventional solid-state reaction method. Ultraviolet-visible-near-infrared (UV-Vis-NIR) diffuse reflectance spectroscopy revealed that the optical band gap values of this material at ambient conditions are 3.77 and 3.35 eV for direct and indirect transition, respectively. We also report the electrical properties of the sample using alternating current (AC) complex impedance spectroscopy (CIS) technique over a frequency range of 40 Hz to 5 MHz at several temperatures in the range 693–883 K. These studies showed that temperature dependence of the direct current (DC) conductivity (σdc) and the relaxation frequency (fr) obey the Arrhenius law. However, the obtained values of the activation energy are different, confirming that ionic transport in the material is not due to a simple hopping mechanism. Based on DC conductivity data, NaAl(MoO4)2 can be classified as low ionic conductor. The differential thermal analysis (DTA) shows the presence of a structural phase transition at 580 °C, which is confirmed by the variation of fr and σdc as a function of temperature. The bond valence sum map (BVSM) analysis indicates that the sodium ions seem to be trapped in their own sites. Consequently, the Na+ ion transport in the interlayer spaces is very difficult.

Multiple summing maps: Coordinatewise summability, inclusion theorems and p-Sidon sets

We discuss the multiple summability of a multilinear map T:X1×⋯×Xm→Y when we have information on the summability of the maps it induces on each coordinate. Our methods have applications to inclusion theorems for multiple summing multilinear mappings and to the product of p-Sidon sets.

Sodium layer chiral distribution and spin structure of Na2Ni2TeO6 with a Ni honeycomb lattice

The nature of Na ion distribution, diffusion path, and the spin structure of $P2$-type Na$_2$Ni$_2$TeO$_6$ with a Ni honeycomb network has been explored. The nuclear density distribution of Na ions reveals a 2D chiral pattern within Na layers without breaking the original 3D crystal symmetry, which has been achieved uniquely via an inverse Fourier transform (iFT)-assisted neutron diffraction technique. The Na diffusion pathway described by the calculated iso-surface of Na ion bond valence sum (BVS) map is found consistent to a chiral diffusion mechanism. The Na site occupancy and Ni$^{2+}$ spin ordering were examined in detail with the electron density mapping, neutron diffraction, magnetic susceptibility, specific heat, thermal conductivity and transport measurements. Signatures of both strong incommensurate (ICM) and weak commensurate (CM) antiferromagnetic (AFM) spin ordering were identified in the polycrystalline sample studied, and the CM-AFM spin ordering was confirmed by using a single crystal sample through the $k$-scan in the momentum space corresponding to the AFM peak of ($\frac{1}{2}$, 0, 1).

Probing surface valence, magnetic property, and oxide ion diffusion pathway in B-site ordered perovskite-type Ba2Ca0.67M0.33NbO6 − δ (M[dbnd]Mn, Fe, Co)

Here, we report the valence of transition metals at surface, magnetic ordering and oxide-ion transport pathway of the double perovskite-type Ba2Ca0.67M0.33NbO6−δ (MMn, Fe, Co). In-situ X-ray photoelectron spectroscopy (XPS) reveals that the surface valences for Mn and Co-doped Ba2Ca0.67M0.33NbO6−δ are 2.5+ and 2+, respectively at 700°C. All the Ba2Ca0.67M0.33NbO6−δ samples are paramagnetic with no long-range cooperative interaction between individual spins. Bond valence sum (BVS) map and molecular dynamics (MD) reveal that the oxide ion migration pathways are isotropic in all investigated Ba2Ca0.67M0.33NbO6−δ. In particular, MD simulations (≥800K) show a long-range oxide ion transport with an activation energy of 0.69eV for Ba2Ca0.67Co0.33NbO6−δ.

New types of Lipschitz summing maps between metric spaces

Building upon the results of M. C. Matos and extending previous work of J. D. Farmer, W. B. Johnson and J. A. Chavez-Dominguez we define a Lipschitz mixed summable sequence as the pointwise product of a strongly summable sequence and a weakly Lipschitz summable one. Then we introduce classes of Lipschitz maps satisfying inequalities between Lipschitz mixed summable sequence and strongly summable sequences analogously to the linear case. These classes generalize the classes of Lipschitz summable maps considered earlier in the literature. We use standard techniques to establish several basic properties, showing that these classes of maps are ideals and some relationships between them. We establish various composition and inclusion theorems between different classes of Lipschitz summing maps and several characterizations. Furthermore, we prove that the classes of Lipschitz p-summing maps coincide and the nonlinear “Pietsch Domination Theorem” for the case 0<p<1. We also identify cases where all Lipschitz maps are in the aforementioned classes of Lipschitz maps and discuss a sufficient condition for a Lipschitz composition formula as in the linear case.

Exploration of a Metastable Normal Spinel Phase Diagram for the Quaternary Li–Ni–Mn–Co–O System

In an attempt to enlarge the normal spinel phase diagram for the quaternary Li–Ni–Mn–Co–O system, the transformation at moderate temperatures (150–210 °C) of layered Li0.5(Ni1–y–zMnyCoz)O2 (R3̅m), which were obtained by an ambient-temperature extraction of lithium from Li0.5(Ni1–y–zMnyCoz)O2, into normal spinel-like (Fd3̅m) Li(Ni1–y–zMnyCoz)2O4 has been investigated. The phase-conversion mechanism has been studied by joint time-of-flight (TOF) neutron and X-ray diffractions, thermogravimetric analysis, and bond valence sum map. The ionic diffusion of lithium (3a, 6c) and nickel (3a, 3b) ions has been quantified as a function of temperature. The investigated spinel phases are metastable, and they are subject to change into rock-salt phases at higher temperatures. The phases have been characterized as cathodes in lithium-ion cells. The study may serve as a strategic model to access other metastable phases by low-temperature synthesis approaches.

β-NaVOPO4 Obtained by a Low-Temperature Synthesis Process: A New 3.3 V Cathode for Sodium-Ion Batteries

Vanadyl phosphates (VOPO4) represent a class of attractive cathodes in lithium-ion batteries. However, the exploration of this type of materials in sodium-ion batteries is rare. Here, we report for the first time the synthesis of orthorhombic β-NaVOPO4 by first chemically extracting lithium from β-LiVOPO4 and then inserting sodium into the obtained β-VOPO4 by a microwave-assisted solvothermal process with NaI, which serves both as a reducing agent and sodium source. Intermediate NaxVOPO4 compositions with x = 0.3, 0.5, and 0.8 have also been obtained by controlling the amount of NaI in the reaction mixture. Joint Rietveld refinement of synchrotron X-ray diffraction (XRD) and neutron diffraction confirms that the fully sodiated β-NaVOPO4 is isostructural with the lithium counterpart β-LiVOPO4. Bond valence sum maps suggest that sodium ions possibly diffuse along the [010] direction in the lattice, similar to the ionic conduction pathway in β-LiVOPO4. Although the initial discharge capacity is low due to th...