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In this paper, we present an explicit description of finite transcendence bases in the differential field of differential rational functions that are invariant under the action of the Galilean transformation group in a real finite-dimensional space. Necessary and sufficient conditions of the equivalence of paths in the n-dimensional Galilean space are obtained.

In this paper, we study the class of laterally complete commutative unital regular algebras A over arbitrary fields. We introduce a notion of passport Γ(X) for a faithful regular laterally complete A- modules X, which consist of uniquely defined partition of unity in the Boolean algebra of all idempotents in A and of the set of pairwise different cardinal numbers. We prove that A-modules X and Y are isomorphic if and only if Γ(X)= Γ(Y ). Further we study Banach A-modules in the case A = C∞(Q) or A = C∞(Q)+ i · C∞(Q). We establish the equivalence of all norms in a finite-dimensional (respectively, σ-finite-dimensional) A-module and prove an A-version of Riesz Theorem, which gives the criterion of a finite-dimensionality (respectively, σ-finite-dimensionality) of a Banach A-module.

In this paper, we review the results on topological ∗-algebras S(M), S(M, τ), and LS(M) of measurable, τ -measurable, and locally measurable operators affiliated with the von Neumann algebra M. Also, we consider relations between those algebras for different classes of von Neumann algebras and establish the continuity of operator-valued functions with respect to the local convergence in measure. We describe maximal commutative ∗-subalgebras of the algebra LS(M) as well.

Let G be a subgroup in the group of all invertible linear transformations of a finite-dimensional real space X. One of the problems in differential geometry is that of finding easily verified necessary and sufficient conditions for G-equivalence of paths in X. In solving this problem, we use methods of the theory of differential invariants which give descriptions of transcendence bases of differential fields of G-invariant differential rational functions. Having explicit forms of transcendence bases, we can obtain efficient criteria for G-equivalence of paths with respect to actions of the special linear, orthogonal, pseudoorthogonal, and symplectic groups. We present a description of one finite transcendence basis in the differential field of differential rational functions invariant with respect to the action of the pseudo-Galilean group ΓO. Based on this, we establish necessary and sufficient conditions of ΓO-equivalence of paths.

It is known that, for a positive Dunford-Schwartz operator in a noncommutative $L^p$-space, $1\leq p, Comment: arXiv admin note: substantial text overlap with arXiv:1607.03452

We show that if a σ-finite infinite measure space ( Ω , μ ) is quasi-non-atomic, then the Dunford–Schwartz pointwise ergodic theorem holds for f ∈ L 1 ( Ω ) + L ∞ ( Ω ) if and only if μ { | f | ≥ λ } ∞ for all λ > 0 .

We consider a complex symmetric sequence space E that possesses the Fatou property and is different from l2. We prove that, for every surjective linear isometry V on E, there exist λ n ∈ ℂ with |λ n | = 1 and a bijective mapping π on the set ℕ of natural numbers such that $$V\left( {\left\{ {\xi _n } \right\}_{n \in \mathbb{N}} } \right) = \left\{ {\lambda _n \xi _{\pi (n)} } \right\}_{n \in \mathbb{N}}$$ for every {ξ n {n∈ℕ ∈ E.

We prove a version of Blum–Hanson ergodic theorem for ( L 1 , L ∞ ) -contractions acting in noncommutative symmetric spaces with order continuous norm. A similar result is established for arbitrary contractions on Hardy subspaces of p-convex Schatten ideals of compact operators.

The goal of this study is to examine (1) whether and how the F0 contour of a sequence of neutral tones in Standard Mandarin is affected by the following full tone due to anticipatory tonal coarticulation, (2) whether and how the degree of anticipatory tonal coarticulation varies as a function of the strength of an intervening boundary, and (3) whether boundary-conditioned anticipatory tonal coarticulatory variations can be accounted for by boundary-induced durational changes. By using generalized additive mixed models to analyze time-varying F0 contours of neutral-tone sequence, we are able to formally detect anticipatory tonal coarticulation effects across different boundary conditions while simultaneously taking into account individual variations of 20 speakers. Results show that (a) F0 contours of neutral-tone sequence can be affected by both assimilatory and dissimilatory anticipatory effects and anticipation could spread to non-adjacent neutral tones, that (b) anticipatory tonal coarticulation becomes weaker when crossing a strong boundary than when crossing a weak boundary, and that (c) boundary-induced anticipatory tonal coarticulation reduction cannot be simply accounted for by boundary-induced lengthening effect. Based on the results, we argue that the anticipatory tonal coarticulation patterns reported in this study are more consistent with the soft template mark-up language (Stem-ML) model than with the parallel encoding and target approximation (PENTA) model, and that boundary-induced anticipatory tonal coarticulation reduction is primarily the result of active speech planning.

We show that ergodic flows in the noncommutative [Formula: see text]-space (associated with a semifinite von Neumann algebra) generated by continuous semigroups of positive Dunford–Schwartz operators and modulated by bounded Besicovitch almost periodic functions converge almost uniformly. The corresponding local ergodic theorem is also proved. We then extend these results to arbitrary noncommutative fully symmetric spaces and present applications to noncommutative Orlicz (in particular, noncommutative [Formula: see text]-spaces), Lorentz, and Marcinkiewicz spaces. The commutative counterparts of the results are derived.

Local mean and individual (with respect to almost uniform convergence in Egorov’s sense) ergodic theorems are established for actions of the semigroup $${\mathbb {R}}_+^d$$ in symmetric spaces of measurable operators associated with a semifinite von Neumann algebra.

Let $${(\Omega,\mu)}$$ be a $${\sigma}$$ -finite measure space, and let $${X \subset L^{1}(\Omega)+ L^{\infty}(\Omega)}$$ be a fully symmetric space of measurable functions on $${(\Omega,\mu)}$$ . If $${{\mu(\Omega)=\infty}}$$ , necessary and sufficient conditions are given for almost uniform convergence in X (in Egorov’s sense) of Cesaro averages $${M_n(T)(f)=\frac{1}{n} \sum_{k = 0}^ {n-1} T^k(f)}$$ for all Dunford–Schwartz operators T in $${L^{1}(\Omega)+ L^{\infty}(\Omega)}$$ and any $${f\in X}$$ . If $${(\Omega,\mu)}$$ is quasi-non-atomic, it is proved that the averages $${M_n(T)}$$ converge strongly in X for each Dunford–Schwartz operator T in $${L^{1}(\Omega)+ L^{\infty}(\Omega)}$$ if and only if X has order continuous norm and $${L^1(\Omega)}$$ is not contained in X.

We consider a system of matrix differential equations whose nondegenerate solutions are O(n, p, R)-equivalent, where O(n, p, R) is the pseudo-orthogonal group of invertible linear transformations of \(R^n\). We show that the class of first columns of the set of matrices that are nondegenerate solutions of this system coincides with the class of O(n, p, R)-equivalent paths in \(R^n\).

Let \((\varOmega ,\mu )\) be a \(\sigma \)-finite measure space, and let \(L_0(\varOmega , \mu )\) be the \(*\)-algebra of all complex (real) valued measurable functions on \((\varOmega ,\mu )\). The \(*\)-subalgebra \(L_{\log }(\varOmega , \mu )=\{f \in L_0(\varOmega , \mu ): \int \limits _{\varOmega } \log (1+|f|)d\mu < + \infty \} \) of \(L_0(\varOmega , \mu )\) is called the algebra of log-integrable measurable functions on \((\varOmega ,\mu )\). Using the notion of passport of a normed Boolean algebra, we give the necessary and sufficient conditions for a \(*\)-isomorphism of two algebras of log-integrable measurable functions.

We prove that every derivation acting on a von Neumann algebra M with values in a quasi-normed bimodule of locally measurable operators affiliated with M is necessarily inner.

It is proved that for every surjective linear isometry $V$ on a perfect Banach symmetric ideal $\mathcal C_E\neq \mathcal C_2$ of compact operators, acting in a complex separable infnite-dimensional Hilbert space $\mathcal H$ there exist unitary operators $u$ and $v$ on $\mathcal H$ such that $V(x)=uxv$ or $V(x) = ux^tv$ for all $x\in \mathcal C_E$, where $x^t$ is the transpose of an operator $x$ with respect to a fixed orthonormal basis in $\mathcal H$. In addition, it is shown that any surjective 2-local isometry on a perfect Banach symmetric ideal $\mathcal C_E \neq \mathcal C_2$ is a linear isometry on $\mathcal C_E$.

It is proved that every continuous derivation on the *-algebra S(M, τ) of all τ-measurable operators affiliated with a von Neumann algebra M is inner. For every properly infinite von Neumann algebra M, any derivation on the *-algebra S(M, τ) is inner.

LetA be a commutativeAW*-algebra.We denote by S(A) the *-algebra of measurable operators that are affiliated with A. For an ideal I in A, let s(I) denote the support of I. Let Y be a solid linear subspace in S(A). We find necessary and sufficient conditions for existence of nonzero band preserving derivations from I to Y. We prove that no nonzero band preserving derivation from I to Y exists if either Y ⊂ Aor Y is a quasi-normed solid space. We also show that a nonzero band preserving derivation from I to S(A) exists if and only if the boolean algebra of projections in the AW*-algebra s(I)A is not σ-distributive.

We extend the Fuglede-Putnam theorem from the algebra $B(H)$ of all bounded operators on the Hilbert space $H$ to the algebra of all locally measurable operators affiliated with a von Neumann algebra., 11 pages

We prove that any derivation of the *-algebra \({LS({\mathcal{M}})}\) of all locally measurable operators affiliated with a properly infinite von Neumann algebra \({{\mathcal{M}}}\) is continuous with respect to the local measure topology \({t({\mathcal{M}})}\) . Building an extension of a derivation \({\delta:{\mathcal{M}}\rightarrow LS({\mathcal{M}})}\) up to a derivation from \({LS({\mathcal{M}})}\) into \({LS({\mathcal{M}})}\) , it is further established that any derivation from \({{\mathcal{M}}}\) into \({LS({\mathcal{M}})}\) is \({t({\mathcal{M}})}\) -continuous.

For a noncommutative Orlicz space associated with a semifinite von Neumann algebra, a faithful normal semifinite trace and an Orlicz function satisfying \((\delta _2,\Delta _2)\)-condition, an individual ergodic theorem is proved.

We present versions of ergodic theorems for L1-L∞ contractions in Banach–Kantorovich Lp-lattices associated with the disjunctive decomposable measure taking values in the algebra of measurable functions.

The problems of mathematical biology, as a rule, are formulated in terms of independent and depended (unknown) variables (functions), and operators (mostly differential operators). These variables belong to some spaces and operators acting in these spaces. Both, unknown variables and operators, follow the main rules of these spaces as metrics, topology and etc. In applications a solution of the problem will be constructed by approximation methods based on metrics/topology of the space. In this convergence of the constructed approximations essentially depends on compactness.

We consider the local measure topology \({t(\mathcal{M})}\) on the ⁎-algebra \({LS(\mathcal{M})}\) of all locally measurable operators and on the ⁎-algebra \({S(\mathcal{M},\tau)}\) of all τ-measurable operators affiliated with a von Neumann algebra \({\mathcal{M}}\). If τ is a semifinite but not a finite trace on \({\mathcal{M},}\) then one can consider the τ-local measure topology tτ l and the weak τ-local measure topology twτ l. We study relationships between the topology \({t(\mathcal{M})}\) and the topologies tτ l, twτ l, and the (o)-topology \({t_o(\mathcal{M})}\) on \({LS_h(\mathcal{M})=\{T\in LS(\mathcal{M}): T^\ast=T\}}\). We find that the topologies \({t(\mathcal{M})}\) and tτ l (resp. \({t(\mathcal{M})}\) and twτ l) coincide on \({S(\mathcal{M},\tau)}\) if and only if \({\mathcal{M}}\) is finite, and \({t(\mathcal{M})=t_o(\mathcal{M})}\) on \({LS_h(\mathcal{M})}\) holds if and only if \({\mathcal{M}}\) is a σ-finite and finite. Moreover, it turns out that the topology tτl (resp. twτ l) coincides with the (o)-topology on \({S_h(\mathcal{M},\tau)}\) only for finite traces. We give necessary and sufficient conditions for the topology \({t(\mathcal{M})}\) to be locally convex (resp., normable). We show that (o)-convergence of sequences in \({LS_h(\mathcal{M})}\) and convergence in the topology \({t(\mathcal{M})}\) coincide if and only if the algebra \({\mathcal{M}}\) is an atomic and finite algebra.

We show that a Banach Principle for L ∞ suggested by A. Bellow and R.L. Jones can be extended to the case of semifinite measure.

In this paper we consider traces on a von Neumann algebra M with values in complex Kantorovich-Pinsker spaces. We establish the connection between the convergence with respect to the trace and the convergence locally in measure in the algebra S(M) of measurable operators affiliated with M. We define the (bo)-complete lattice-normed spaces of integrable operators in S(M) and prove that they are decomposable if the trace possesses the Maharam property.

We obtain some versions of ergodic theorems for positive contractions in the Orlicz-Kantorovich lattices L M (m) associated with a measure m taking values in the algebra of measurable real functions. The proof is carried out by representing L M (m) as measurable bundles of classical Orlicz function spaces.

We consider the topology $$ t\left( \mathcal{M} \right) $$ of convergence locally in measure in the *-algebra $$ LS\left( \mathcal{M} \right) $$ of all locally measurable operators affiliated to the von Neumann algebra $$ \mathcal{M} $$ . We prove that $$ t\left( \mathcal{M} \right) $$ coincides with the (o)-topology in $$ L{S_h}\left( \mathcal{M} \right) = \left\{ {T \in LS\left( \mathcal{M} \right):T* = T} \right\} $$ if and only if the algebra $$ \mathcal{M} $$ is σ-finite and is of finite type. We also establish relations between $$ t\left( \mathcal{M} \right) $$ and various topologies generated by a faithful normal semifinite trace on $$ \mathcal{M} $$ .

Decomposable L0-valued measures on a complete Boolean algebra B are considered. Criterion for B to be representable as a measurable bundle of continuous (respectively, atomic) Boolean algebras is given.

In the paper, the *-algebras of measurable operators, locally measurable operators, and τ-measurable operators associated with a von Neumann algebra M are considered. Conditions under which some of these algebras coincide are given. Bibliography: 11 titles.

We describe models of Mandarin prosody that allow us to make quantitative measurements of prosodic strengths. These models use Stem-ML, which is a phenomenological model of the muscle dynamics and planning process that controls the tension of the vocal folds, and therefore the pitch of speech. Because Stem-ML describes the interactions between nearby tones, we were able to capture surface tonal variations using a highly constrained model with only one template for each lexical tone category, and a single prosodic strength per word. The model accurately reproduces the intonation of the speaker, capturing 87% of the variance of f 0 with these strength parameters. The result reveals alternating metrical patterns in words, and shows that the speaker marks a hierarchy of boundaries by controlling the prosodic strength of words. The strengths we obtain are also correlated with syllable duration, mutual information and part-of-speech.

We study the relationship between (o)-convergence and almost-everywhere convergence in the Hermite part of the ring of unbounded measurable operators associated with a finite von Neumann algebra. In particular, we prove a theorem according to which (o)-convergence and almost-everywhere convergence are equivalent if and only if the von Neumann algebra is of the type I.

This paper examined the articulatory properties of high vowels [i], [y], and [u] in Mandarin produced by four Taiwanese Mandarin native speakers and four English-speaking Chinese learners (L2 learners) with an Electromagnetic Articulagroph AG500. The articulatory positions of the tongue top (TT), the tongue body (TB), the tongue dorsal (TD), and the lips were investigated. The TT, TB, and TD of [y] produced by the L2 learner were further back than that by the native. In addition, the TD of [y] by the L2 learners was higher than the native. Further comparison found that the tongue positions of [y] was similar to [u] in L2 production. Regarding to the lip positions, the [y] and [u] were more protruded that [i] in the native production, while there is no difference among these three vowels in the L2 production. The findings suggested that most of the L2 learner were not aware that the lingual target [y] should be very similar to [i] but the lip articulators of [y] are more protruded than [i]. Some L2 learner...