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Background Continuity of care is positively associated with beneficial patient outcomes. Data on the level of continuity of care in the ambulatory setting in Switzerland are lacking. Aim The aim of this study was to evaluate continuity of care in Swiss cancer patients based on routine data of mandatory health insurance using four established continuity scales. Methods Retrospective analysis of Swiss claims data (N=23'515 patients with incident use of antineoplastics). The Usual Provider Continuity score, the Modified Modified Continuity Index, the Continuity of Care index, and the Sequential Continuity Index were analyzed based on consultations with general practitioners (GPs), physician specialists and ambulatory hospital wards. Results Using information of health insurance claims, the number of consultations and the general level of continuity of care in Swiss cancer patients are high. Continuity of care scores were significantly associated with sociodemographic and regional factors. When focusing on consultations with GPs only, all four scores consistently showed high values indicating high levels of continuity. Continuity with general practitioners was associated with lower costs and lower risks for hospitalization and death. Conclusion This is the first study giving insight into continuity of care in Swiss cancer patients. The present study shows that continuity of care is measurable using health insurance claims data. It indicates that continuity with general practitioners is associated with a beneficial outcome.

This note provides 4 equivalent conditions with the continuity of relations adopted by Brattka and Hertling to investigate computability of relations. As the case of continuous functions, each condition characterlises continuous relations by respectively using open sets, neighbourhoods, closures, and closed sets. A notion of sequential continuity is also studied. We show a relevance between continuous relations and sequentially continuous relations which is, again, analogous to the case of functions.

In this paper we study from a qualitative point of view the nonlinear singular Dirichlet problem depending on a parameterλ> 0 that was considered in [32]. Denoting bySλthe set of positive solutions of the problem corresponding to the parameterλ, we establish the following essential properties ofSλ:there exists a smallest element$\begin{array}{} u_\lambda^* \end{array}$inSλ, and the mappingλ↦$\begin{array}{} u_\lambda^* \end{array}$is (strictly) increasing and left continuous;the set-valued mappingλ↦Sλis sequentially continuous.

In the present paper, we establish some fixed-point theorems for a $$2\times 2$$ block operator matrix involving multivalued maps acting on Banach spaces. These results are formulated in terms of weak sequential continuity and the technique of measures of weak noncompactness. The results obtained are then applied to a coupled system of nonlinear equations.

Açıkgöz, Ahu (Balikesir Author), Continuity is one of most important concepts in many mathematical disciplines. In some situations general notion of continuity is replaced by sequential continuity. Connor and Grosse-Erdmann replaced lim in the definition of sequential continuity of real functions by a linear functional G on a linear subspace of the vector space of all real sequences. Their definition was extended to topological group X by replacing a linear functional G with an additive function defined on a subgroup of the group of all X-valued sequences. In this paper we introduce neutrosophic G-continuity and investigate its properties in neutrosophic topological spaces.

Objective To determine the extent of longitudinal continuity of care (CoC) during pregnancy and delivery in the Volta Region of Ghana. Methods Longitudinal data were used from the National Health Insurance Claims Dataset for the period January to December 2013 for pregnant women who sought antenatal and delivery care in the region. Pregnant women who delivered at a health facility with at least three visits were included in the study. Five CoC indices were calculated for each pregnant woman. Results Of the 14 474 pregnant women included in the study, 58.4% had perfect CoC. Mean CoC indices were: most frequent provider continuity (MFPC) 0.82 ± 0.25; modified, modified continuity index (MMCI) 0.86 ± 0.20; continuity of care index (COCI) 0.76 ± 0.30; sequential continuity index (SECON) 0.80 ± 0.28; and place of delivery continuity (PDC) 0.68 ± 0.41. Conclusion There are relatively medium to high levels of CoC indices during pregnancy and delivery, with place of delivery CoC having the lowest score, an indication that more pregnant women switched providers during delivery. There is a need for policy to ensure CoC during pregnancy.

We make progress on a problem of R. Coifman, P.-L. Lions, Y. Meyer, and S. Semmes from 1993 by showing that the Jacobian operator $J$ does not map $W^{1,n}(\mathbb R^n,\mathbb R^n)$ onto the Hardy space $\mathcal{H}^1(\mathbb R^n)$ for any $n \ge 2$. The related question about surjectivity of $J \colon \dot{W}^{1,n}(\mathbb R^n,\mathbb R^n) \to \mathcal{H}^1(\mathbb R^n)$ is still open. The second main result and its variants reduce the proof of $\mathcal{H}^1$ regularity of a large class of compensated compactness quantities to an integration by parts or easy arithmetic, and applications are presented. Furthermore, we exhibit a class of nonlinear partial differential operators in which weak sequential continuity is a strictly stronger condition than $\mathcal{H}^1$ regularity, shedding light on another problem of Coifman, Lions, Meyer, and Semmes., Comment: 29 pages; added one reference and an acknowledgement, changed an inequality on p. 27 into a two-sided estimate

We characterize generalized Young measures, the so-called DiPerna–Majda measures which are generated by sequences of gradients. In particular, we precisely describe these measures at the boundary of the domain in the case of the compactification of ℝm × n by the sphere. We show that this characterization is closely related to the notion of quasiconvexity at the boundary introduced by Ball and Marsden [J.M. Ball and J. Marsden, Arch. Ration. Mech. Anal. 86 (1984) 251–277]. As a consequence we get new results on weak W 1,2 (Ω ; ℝ3 ) sequential continuity of u → a · [Cof∇u ] ϱ , where Ω ⊂ ℝ3 has a smooth boundary and a,ϱ are certain smooth mappings.

Let us recall that an operator $T:E\rightarrow F,$ between two Banach lattices, is said to be weak* Dunford-Pettis (resp. weak almost limited) if $f_{n}\left( Tx_{n}\right) \rightarrow 0$ whenever $(x_{n})$ converges weakly to $0$ in $E$ and $(f_{n})$ converges weak* to $0$ in $F^{\prime }$ (resp. $f_{n}\left( Tx_{n}\right) \rightarrow 0$ for all weakly null sequences $\left( x_{n}\right) \subset E$ and all weak* null sequences $\left(f_{n}\right) \subset F^{\prime }$ with pairwise disjoint terms). In this note, we state some sufficient conditions for an operator $R:G\rightarrow E$(resp. $S:F\rightarrow G$), between Banach lattices, under which the product $TR$ (resp. $ST$) is weak* Dunford-Pettis whenever $T:E\rightarrow F$ is an order bounded weak almost limited operator. As a consequence, we establish the coincidence of the above two classes of operators on order bounded operators, under a suitable lattice operations' sequential continuity of the spaces (resp. their duals) between which the operators are defined. We also look at the order structure of the vector space of weak almost limited operators between Banach lattices.

Multidisciplinary treatment and continuity of care throughout treatment are important for ensuring metabolic control and avoiding complications in diabetic patients. This study examines the relationship between continuity of care of the treating disciplines and clinical evolution of patients. Data from 1836 adult patients experiencing type 2 diabetes mellitus were analyzed, in a period between 12 and 24 months. Continuity was measured by using four well known indices: Usual Provider Continuity (UPC), Continuity of Care Index (COCI), Herfindahl Index (HI), and Sequential Continuity (SECON). Patients were divided into five segments according to metabolic control: well-controlled, worsened, moderately decompensated, highly decompensated, and improved. Well-controlled patients had higher continuity by physicians according to UPC and HI indices (p-values 0.029 and &lt, 0.003), whereas highly decompensated patients had less continuity in HI (p-value 0.020). Continuity for nurses was similar, with a greater continuity among well-controlled patients (p-values 0.015 and 0.001 for UPC and HI indices), and less among highly decompensated patients (p-values 0.004 and &lt, 0.001 for UPC and HI indices). Improved patients had greater adherence to the protocol than those who worsened. The SECON index showed no significant differences across the disciplines. This study identified a relationship between physicians and nurse&rsquo, s continuity of care and metabolic control in patients with diabetes, consistent with qualitative findings that highlight the role of nurses in treatment.

We consider notions of boundedness of subsets of the natural numbers ℕ that occur when doing mathematics in the context of intuitionistic logic. We obtain a new characterization of the notion of a pseudobounded subset and we formulate the closely related notion of a detachably finite subset. We establish metric equivalents for a subset of ℕ to be detachably finite and to satisfy the ascending chain condition. Following Ishihara, we spell out the relationship between detachable finiteness and sequential continuity. Most of the results do not require countable choice. (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

WOS: 000219434000018, We study contunity type properties of factorable double functions defined on a double subset A x A of R-2 into R, and obtain interesting results related to uniform continuity sequential continuity, continuity, and a newly introduced type of continuity of factorable double functions defined on a double subset A x A of R-2 into R.

The main purpose of this Note is to show how a ‘nonlinear Korn's inequality on a surface’ can be established. This inequality implies in particular the following interesting per se sequential continuity property for a sequence of surfaces. Let ω be a domain in R 2 , let θ : ω ¯ → R 3 be a smooth immersion, and let θ k : ω ¯ → R 3 , k ⩾ 1 , be mappings with the following properties: They belong to the space H 1 ( ω ) ; the vector fields normal to the surfaces θ k ( ω ) , k ⩾ 1 , are well defined a.e. in ω and they also belong to the space H 1 ( ω ) ; the principal radii of curvature of the surfaces θ k ( ω ) stay uniformly away from zero; and finally, the three fundamental forms of the surfaces θ k ( ω ) converge in L 1 ( ω ) toward the three fundamental forms of the surface θ ( ω ) as k → ∞ . Then, up to proper isometries of R 3 , the surfaces θ k ( ω ) converge in H 1 ( ω ) toward the surface θ ( ω ) as k → ∞ . To cite this article: P.G. Ciarlet et al., C. R. Acad. Sci. Paris, Ser. I 341 (2005).

Examples of completeD-metric spaces are given in which every convergent sequence has at most two limits and in which there are convergent sequences with exactly two limits. Also an example of a completeD-metric space having a convergent sequence with infinitely many limits is given and, using the example, several fixed point theorems inD-metric spaces are shown to be false. Modifications of some of these theorems and their generalizations are obtained either by imposing restrictions on the number of limits of certain convergent sequences in the space or by assuming the sequential continuity of theD-metric in any two variables and the theorems so obtained are illustrated by means of examples.

In this paper we prove an existence theorem for the Cauchy problem $$x'\left( t \right) = f\left( {t,x\left( t \right)} \right),x\left( 0 \right) = x_0 ,t \in I_\alpha = \left[ {0,\alpha } \right]$$ using the Henstock-Kurzweil-Pettis integral and its properties. The requirements on the function f are not too restrictive: scalar measurability and weak sequential continuity with respect to the second variable. Moreover, we suppose that the function f satisfies some conditions expressed in terms of measures of weak noncompactness.

Let P : E → K be an N-homogeneous polynomial, where E is a Banach space over K = R or C . We study properties of the set Cp = {x ∈ E : P is weakly sequentially continuous at x}.

We describe dualities related to the foundations of probability theory in which sequential convergence and sequential continuity play an important role.

We study topological and categorical aspects of the extension of σ -additive measures from a field of sets to the generated σ -field within a category of Boolean algebras carrying initial sequential convergences with respect to 2 -valued homomorphisms. We describe the relationship between σ -additivity and sequential continuity of finitely additive measures. A key role is played by the epireflective subcategory of absolutely sequentially closed objects. In case of fields of sets such objects are exactly σ -fields. The results provide information about basic notions of probability theory: events, probability measures, and random functions.

Submeasurable cardinals are defined in a similar way as measurable cardinals are. Their characterizations are given by means of sequentially continuous pseudonorms (or homomorphisms) on topological groups and of sequentially continuous (or uniformly continuous) functions on Cantor spaces (for that purpose it is proved that if a complete Boolean algebra admits a nonconstant sequentially continuous function, it admits a Maharam submeasure).

We show weak* in measures on $\bar\O$/ weak-$L^1$ sequential continuity of $u\mapsto f(x,\nabla u):W^{1,p}(\O;\R^m)\to L^1(\O)$, where $f(x,\cdot)$ is a null Lagrangian for $x\in\O$, it is a null Lagrangian at the boundary for $x\in\partial\O$ and $|f(x,A)|\le C(1+|A|^p)$. We also give a precise characterization of null Lagrangians at the boundary in arbitrary dimensions. Our results explain, for instance, why $u\mapsto \det\nabla u:W^{1,n}(\O;\R^n)\to L^1(\O)$ fails to be weakly continuous. Further, we state a new weak lower semicontinuity theorem for integrands depending on null Lagrangians at the boundary. The paper closes with an example indicating that a well-known result on higher integrability of determinant \cite{Mue89a} need not necessarily extend to our setting. The notion of quasiconvexity at the boundary due to J.M. Ball and J. Marsden is central to our analysis., Comment: arXiv admin note: substantial text overlap with arXiv:1009.0795

The paper gives a characterization of the Dunford-Pettis property of a Banach Space in terms of the joint weak sequential continuity of a composition mapping.

This paper deals, constructively, with two theorems on the sequential continuity of linear mappings. The classical proofs of these theorems use the boundedness of the linear mappings, which is a constructively stronger property than sequential continuity; and constructively inadmissable versions of the Banach-Steinhaus theorem. 1.) Proceedings of the First Japan-New Zealand Workshop on Logic in Computer Science, special issue editors D.S. Bridges, C.S. Calude, M.J. Dinneen and B. Khoussainov.