Fuzzy bases and the fuzzy dimension of fuzzy vector spaces

In this paper, new definitions of a fuzzy basis and a fuzzy dimension for a fuzzy vector space are presented. A fuzzy basis for a fuzzy vector space $(E,mu)$ is a fuzzy set $beta$ on $E$. The cardinality of a fuzzy basis $beta$ is called the fuzzy dimension of $(E,mu)$. The fuzzy dimension of a finite dimensional fuzzy vector space is a fuzzy natural number. For a fuzzy vector space, any two fuzzy bases have the same cardinality. If $widetilde{E}_1$ and $widetilde{E}_2$ are two fuzzy vector spaces, then $dim(widetilde{E}_1+widetilde{E}_2)+dim(widetilde{E}_1cap widetilde{E}_2)=dim(widetilde{E}_1) +dim(widetilde{E}_2)$ and $dim({widetilde{rm{ker }}f})+dim({widetilde{rm{im }}f})=dim(widetilde{E})$ hold without any restricted conditions. end{abstract

THE CHARTERISTICS OF LOWER LIMB MOMENTS IN BASEBALL PITCHING

The aim of this study was to examine the characteristics of lower limb moments in baseball pitching. Ten senior high school pitchers participated in this study (age: 16.7±0.7 yr; height: 179.1±5.8 cm; body mass: 73.7±8.9 kg). Ten VICON cameras (200Hz) and two Kistler force plates (1000Hz) fixed on a pitching mound were used to collect 3-D kinematic and GRF data. Three successful trials for each subject were used to compute lower limbs joint moments. The results indicated, for the pivot leg, ankle plantarflexor moment, knee and hip adductor moment are the key moments to transform energy to trunk and upper extremities by driving and rotating the knee. For the lead leg, ankle plantarflexor moment and hip flexor moment are the main joint moments to brake upper extremities by a knee extention during baseball pitching

Ediacaran Macro Body Fossils

This paper, Ediacaran Macro Body Fossils, reports a new discovery of well preserved three dimensional macro body fossils of the Ediacaran Period in central YunNan province in the People's Republic of China. These body fossils will enable more detailed and in-depth exploration of the evolution of multi-cellular macro organisms on this planet, whereas in the past, researches could only rely on cast or imprint fossils

Unconventional Superconducting Symmetry in a Checkerboard Antiferromagnet

We use a renormalized mean field theory to study the Gutzwiller projected BCS states of the extended Hubbard model in the large $U$ limit, or the $t$-$t'$-$J$-$J'$ model on a two-dimensional checkerboard lattice. At small $t'/t$, the frustration due to the diagonal terms of $t'$ and $J'$ does not alter the $d_{x^2-y^2}$-wave pairing symmetry, and the negative (positive) $t'/t$ enhances (suppresses) the pairing order parameter. At large $t'/t$, the ground state has an extended s-wave symmetry. At the intermediate $t'/t$, the ground state is $d+id$ or $d+is$-wave with time reversal symmetry broken.Comment: 6 pages, 6 figure

Andreev and Single Particle Tunneling Spectroscopies in Underdoped Cuprates

We study tunneling spectroscopy between a normal metal and underdoped cuprate superconductor modeled by a phenomenological theory in which the pseudogap is a precursor to the undoped Mott insulator. In the transparent tunneling limit, the spectra show a small energy gap associated with Andreev reflection. In the Giaever limit, the spectra show a large energy gap associated with single particle tunneling. Our theory semi-quantitatively describes the two gap behavior observed in tunneling experiments.Comment: 5 pages, 4 figures, submitted to Phys. Rev. Lett. minor changes of reference

OVOR: OnePrompt with Virtual Outlier Regularization for Rehearsal-Free Class-Incremental Learning

Recent works have shown that by using large pre-trained models along with learnable prompts, rehearsal-free methods for class-incremental learning (CIL) settings can achieve superior performance to prominent rehearsal-based ones. Rehearsal-free CIL methods struggle with distinguishing classes from different tasks, as those are not trained together. In this work we propose a regularization method based on virtual outliers to tighten decision boundaries of the classifier, such that confusion of classes among different tasks is mitigated. Recent prompt-based methods often require a pool of task-specific prompts, in order to prevent overwriting knowledge of previous tasks with that of the new task, leading to extra computation in querying and composing an appropriate prompt from the pool. This additional cost can be eliminated, without sacrificing accuracy, as we reveal in the paper. We illustrate that a simplified prompt-based method can achieve results comparable to previous state-of-the-art (SOTA) methods equipped with a prompt pool, using much less learnable parameters and lower inference cost. Our regularization method has demonstrated its compatibility with different prompt-based methods, boosting those previous SOTA rehearsal-free CIL methods' accuracy on the ImageNet-R and CIFAR-100 benchmarks. Our source code is available at https://github.com/jpmorganchase/ovor.Comment: Accepted by ICLR 202

Charge Ordered RVB States in the Doped Cuprates

We study charge ordered d-wave resonating valence bond states (dRVB) in the doped cuprates, and estimate the energies of these states in a generalized $t-J$ model by using a renormalized mean field theory. The long range Coulomb potential tends to modulate the charge density in favor of the charge ordered RVB state. The possible relevance to the recently observed $4 \times 4$ checkerboard patterns in tunnelling conductance in high $T_c$ cuprates is discussed.Comment: 4 pages, 4 figures, 3 table