The Local Theory of Completely 1-Summing Mapping Spaces

In this paper, we investigate local properties in the system of completely 1-summing mapping spaces. We introduce notions of injectivity, local reflexivity, exactness, nuclearity and finite-representability in the system of completely 1-summing mapping spaces. First we obtain that if V has WEP, V is locally reflexive in the system (Ⅱ1(⋅,⋅), π1(⋅)) if and only if it is locally reflexive in the system (Ⅰ(⋅,⋅), t(⋅)). Furthermore we prove that an operator space V ⊆ B(H) is exact in the system (Ⅱ1(⋅,⋅), π1(⋅)) if and only if V is finitely representable in {Mn}n∈N in the system (Ⅱ1(⋅,⋅), π1(⋅)). At last, we show that an operator space V is finitely representable in {Mn}n∈N in the system (Ⅱ1(⋅,⋅), π1(⋅)) if and only if V = C.

LSTM-based lane change prediction using Waymo open motion dataset: The role of vehicle operating space

Lane change prediction is critical for crash avoidance but challenging as it requires the understanding of the instantaneous driving environment.With cutting-edge artificial intelligence and sensing technologies,autonomous vehicles(AVs)are expected to have exceptional perception systems to capture instantaneously their driving environments for predicting lane changes.By exploring the Waymo open motion dataset,this study proposes a framework to explore autonomous driving data and investigate lane change behaviors.In the framework,this study develops a Long Short-Term Memory(LSTM)model to predict lane changing behaviors.The concept of Vehicle Operating Space(VOS)is introduced to quantify a vehicle's instantaneous driving environment as an important indicator used to predict vehicle lane changes.To examine the robustness of the model,a series of sensitivity analysis are conducted by varying the feature selection,prediction horizon,and training data balancing ratios.The test results show that including VOS into modeling can speed up the loss decay in the training process and lead to higher accuracy and recall for predicting lane-change behaviors.This study offers an example along with a methodological framework for transportation researchers to use emerging autonomous driving data to investigate driving behaviors and traffic environments.

THE CENTRAL BMO SPACES AND LITTLEWOOD-PALEY OPERATORS

The authors give a characterization of central bounded mean oscillation space CBMO2(Rγ) in terms of the central Carleson measure. Using this character, the authors establish the CBMO2(Rγ)-boundedness for several classes of general Littlewood-Paley operators.

BOUNDEDNESS OF FRACTIONAL MAXIMAL OPERATOR AND THEIR HIGHER ORDER COMMUTATORS IN GENERALIZED MORREY SPACES ON CARNOT GROUPS

In the article we consider the fractional maximal operator Mα, 0 ≤α 〈 Q on any Carnot group G （i.e., nilpotent stratified Lie group） in the generalized Morrey spaces Mp,φ（G）, where Q is the homogeneous dimension of G. We find the conditions on the pair （φ1, φ2） which ensures the boundedness of the operator Ms from one generalized Morrey space Mp,φ1 （G） to another Mq,φ2 （G）, 1. 〈 p ≤q 〈 ∞. 1/p - 1/q = α/Q, and from the space M1,φ1 （G） to the weak space Wq,φ2 （G）, 1 〈 q 〈 ∞, 1 - 1/q = α/Q. Also find conditions on the φ which ensure the Adams type boundedness of the Ms from M α （G） from Mp,φ^1/p（G）to Mq,φ^1/q（G） for 1 〈p〈q〈∞ and fromM1,φ（G） toWMq,φ^1/q（G）for 1〈q〈∞. In the case b ∈ BMO（G） and 1 〈 p 〈 q 〈 ∞, find the sufficient conditions on the pair （φ1, φ2） which ensures the boundedness of the kth-order commutator operator Mb,α,k from Mp,φ1 （G） to Mq,φ2（G） with 1/p - 1/q = α/Q. Also find the sufficient conditions on the φ which ensures the boundedness of the operator Mb,α,k from Mp,φ^1/p（G） tom Mp,φ^1/p （G） for 1 〈p〈q〈∞. In all the cases the conditions for the boundedness of Mα are given it terms of supremaltype inequalities on （φ1, φ2） and φ , which do not assume any assumption on monotonicity of （φ1, φ2） and φ in r. As applications we consider the SchrSdinger operator -△G ＋ V on G, where the nonnegative potential V belongs to the reverse Holder class B∞（G）. The MB,φ1 - Mq,φ2 estimates for the operators V^γ（-△G ＋ V）^-β and V^γ△↓G（-△G ＋ V）^-β are obtained.

Some New Fixed Point Theorems in Probabilistic Metric Spaces

In this paper, we introduce the concept of the Z-M-PN space and obtain somenew fixed point theorems in probabilistic metric spaces Meanwhile,some famous fixedpoint theorems are generalized in probabilistic metric spaces, such a.s fixed point theorem of Schauder, Guo's theorem and fixed point theorem of Petryshyn are generalized in Menger PN-space. And fixed point theorem of Altman is also generalized in the Z-M-PN space.

SOME ROUGH OPERATORS ON PRODUCT SPACES

In this survey report, we shall mainly summarize some recent progress, interesting problems and typical methods used in the theory related to rough Marcinkiewicz integrals and rough singular integrals on product spaces. In addition, we give new proofs for some known results.

Integrability of the general product Hardy operators on the product Hardy spaces

In this paper,we prove that the general product Hardy operators are bounded from the product Hardy space H1n（Rm1×···×Rmn） to L1（R（∑ni=1mi）.

THE BOUNDEDNESS OF CERTAIN OPERATORS ON HOLDER AND SOBOLEV SPACES

The main topic in this note is to discuss the boundedness of pseudo-differential operators and para-product nptfators on ihe Holder and Sobotev space;, respectively It is the preparation of the thoery of Gibbs - Butzer deffereftital operators and differential equations.

ROUGH OPERATORS AND COMMUTATORS ON HOMOGENEOUS WEIGHTED HERZ SPACES

The authors establish the baundedness on homogeneous weighted Herz spaces for a large class of rough operators and their commutators with BMO functions. In particular, the Calderon-Zygmund singular integrals and the rough R. Fefferman singular integral operators and the rough Ricci-Stein oscillatory singular integrals and the corresponding commutators are considered.

WEIGHTED COMPOSITION OPERATORS BETWEEN BERS-TYPE SPACES AND BERGMAN SPACES

This paper characterizes the boundedness and compactness of weighted composition operators between Bers-type space （or little Bers-type space） and Bergman space. Some estimates for the norm of weighted composition operators between those spaces are obtained.

EXISTENCE OF SOLUTIONS OF A FAMILY OF NONLINEAR BOUNDARY VALUE PROBLEMS IN L^2-SPACES

By using the perturbation results of sums of ranges of accretive mappings of Calvert and Gupta(1978),the abstract results on the existence of solutions of a family of nonlinear boundary value problems in L2(Ω) are studied.The equation discussed in this paper and the methods used here are extension and complement to the corresponding results of Wei Li and He Zhen's previous papers.Especially,some new techniques are used in this paper.

LITTLEWOOD-PALEY OPERATORS AND MARCINKIEWICZ INTEGRAL ON GENERALIZED CAMPANATO SPACES

Littlewood-Paley operators and Marcinkiewicz integral on generalized Campanula spaces ερ,φ are studied. It is proved that the image of a function under the action of these operators is either equal to infinity almost everywhere or is in ερ,φ.

DENSITY PROPERTIES OF MAPPING SPACES FOR OPERATOR SPACES

In this article, we give the sufficient and necessary conditions for which several important mapping spaces are weak＊ dense in the corresponding completely bound mapping spaces.

NOTES ON REAL INTERPOLATION OF OPERATOR L_(p)-SPACES

Let M be a semifinite von Neumann algebra.We equip the associated noncommutative Lp-spaces with their natural operator space structure introduced by Pisier via complex interpolation.On the other hand,for L_(p),p(M)=(L_(∞)(M),L_(1)(M)_(1/p,p)be equipped with the operator space structure via real interpolation as defined by the second named author(J.Funct.Anal.139(1996),500–539).We show that Lp,p(M)=Lp(M)completely isomorphically if and only if M is finite dimensional.This solves in the negative the three problems left open in the quoted work of the second author.We also show that for 1<p<∞and 1≤q≤∞with p 6=q,(L_(∞)(M;l_(q)),L_(1)(M;l_(q)_(1/p,p)=L_(p)(M;l_(q)with equivalent norms,i.e.,at the Banach space level if and only if M is isomorphic,as a Banach space,to a commutative von Neumann algebra.Our third result concerns the following inequality:||(∑iixtq)^(1/q)||lp(M)≤||(∑iixit)^(1/q)||lp(M),for any finite sequence(xi)⊂L+p(M),where 0<r<q<∞and 0<p≤∞.If M is not isomorphic,as a Banach space,to a commutative von Meumann algebra,then this inequality holds if and only if p≥r.

TOEPLITZ-HANKEL TYPE OPERATORS ON PRODUCT SPACES

Via a series of orihogonal two-dimensional wavelets, an orthogonal decomposition of the space of square integral functions on Ux U (U is the upper half-plane) with the meaaure y_1^(_1) y_2~(_2 dx_1 dx_2 dy_1 dy_2 is given. Four kinds of Toeplitz-Hankel type operators between the decomposition components are defined and boundedness. S_p properties of them are established.

BOUNDEDNESS OF MULTILINEAR OPERATORS WITH ROUGH KERNEL ON HERZ SPACES

In this paper,the boundedness of the multilinear operators with rough kernel on the Herz-type spaces is discussed.It is proved that M A,Ω,T A,Ω are bounded on α,p q(Rn) while Mλ A,Ω,TL A,Ω are bounded from α,p 1 q 1(Rn) to α,p 2 q 2(Rn),respectively.

Active Compliance Control of a Position‑Controlled Industrial Robot for Simulating Space Operations

An industrial robot with a six-axis force/torque sensor is usually used to produce a zero-gravity environment for testing space robotic operations.However,using traditional force control methods,such as admittance control,causes position-controlled industrial robots to undergo from force divergence owing to intrinsic time delay.In this paper,a new force control method is proposed to eliminate the force divergence.A hardware-in-the-loop(HIL)simulator with an industrial robot is first presented.The free-floating satellite dynamics and the motion mapping from the satellites to simulator are both established.Thus,the effects of measurement delay and dynamic response delay on contact velocity and force are investigated.After that,a real-time estimation method for contact stiffness and damping is proposed based on the adaptive Kalman filter.The measurement delay is compensated by a phase lead model.Moreover,the identified contact parameters are adopted to modify contact forces,and thus the dynamics response delay can be compensated for.Finally,a co-simulation and experiments were conducted to verify the force control method.The results show that contact stiffness and damping could be identified exactly and that the simulation divergence could be prevented.This paper proposes an active compliance control method that can deal with force constrained tasks of a position-controlled robot in unknown environments.

K-POTENT PRESERVING LINEAR MAPS

Let B(X) be the Banach algebra of all bounded linear operators on a complex Banach space X. Let k greater than or equal to 2 be an integer and phi a weakly continuous linear surjective map from B(X) into itself. It is shown that phi is k-potent preserving if and only if it is k-th-power preserving, and in turn, if and only if it is either an automorphism or an antiautomorphism on B(X) multiplied by a complex number lambda satisfying lambda(k-1) = 1. Let A be a von Neumann algebra and B be a Banach algebra, it is also shown that a bounded surjective linear map from A onto B is k-potent preserving if and only if it is a Jordan homomorphism multiplied by an invertible element with (k - 1)-th power I.

A Generalized Marcinkiewicz Interpolation Theorem and Its Applications

Using a simple method,we generalize Marcinkiewicz interpolation theorem to operators.on Orlicz space and apply it to several important theorems in harmonic analysis.

Analysis on EAST LHCD Operation Space by Using Simple Core-SOL-Divertor Model

A simple core-SOL-divertor model （CSD model） was developed to investigate qual- itatively the overall features of the operational space for the integrated core and edge plasma. In the CSD model, the core plasma model of ITER physics guidelines and the two-point SOL-divertor model are applied, This CSD model is validated by the two dimensional divertor transport code （B2-EIRINE） and by the JT-60U divertor recycling database, and this model is applicable to the low- and high-recycling state of the divertor plasma. The CSD model is applied to the study of the EAST operational space with lower hybrid current drive under various kinds of trade-off for the basic plasma parameters, and the relationship between the operational space and the plasma discharge duration is also discussed.