The inhomogeneous Cauchy-Riemann equation for weighted smooth vector-valued functions on strips with holes

This paper is dedicated to the question of surjectivity of the Cauchy-Riemann operator $$\overline{\partial }$$ ∂ ¯ on spaces $${\mathcal {E}}{\mathcal {V}}(\varOmega ,E)$$ E V ( Ω , E ) of $${\mathcal {C}}^{\infty }$$ C ∞ -smooth vector-valued functions whose growth on strips along the real axis with holes K is induced by a family of continuous weights $${\mathcal {V}}$$ V . Vector-valued means that these functions have values in a locally convex Hausdorff space E over $${\mathbb {C}}$$ C . We derive a counterpart of the Grothendieck-Köthe-Silva duality $${\mathcal {O}}({\mathbb {C}}\setminus K)/{\mathcal {O}}({\mathbb {C}})\cong {\mathscr {A}}(K)$$ O ( C \ K ) / O ( C ) ≅ A ( K ) with non-empty compact $$K\subset {\mathbb {R}}$$ K ⊂ R for weighted holomorphic functions. We use this duality and splitting theory to prove the surjectivity of $$\overline{\partial }:{\mathcal {E}} {\mathcal {V}}(\varOmega ,E)\rightarrow {\mathcal {E}}{\mathcal {V}} (\varOmega ,E)$$ ∂ ¯ : E V ( Ω , E ) → E V ( Ω , E ) for certain E. This solves the smooth (holomorphic, distributional) parameter dependence problem for the Cauchy-Riemann operator on $${\mathcal {E}}{\mathcal {V}}(\varOmega ,{\mathbb {C}})$$ E V ( Ω , C ) .

Therapeutic Methods Including the Tasks of a Nurse and Evaluation of Their Effectiveness in the Opinion of Patients after Craniocerebral Trauma with a Diagnosis of Alcohol use Disorder

Introduction. Alcoholism is a phenomenon with multi-factorial conditions and numerous health and social consequences, which makes its treatment a real challenge not only for the addict himself and his relatives, but also for the entire medical team involved in the therapy process. For this reason, in order to strengthen the therapeutic effects of alcoholic disease, it is important to conduct research aimed at determining the factors that shape the effectiveness of the implemented methods. With this in mind, it has been assumed that the aim of the research is to determine the relationship between the therapeutic methods used in the Clinical Alcohol Dependency Therapy Unit (COTUA), taking into account the tasks of a nurse, and the assessment of their effectiveness in the perception of patients after craniocerebral trauma with a diagnosis of alcohol disease. Material and Methods. 100 COTUA patients were tested, in which the diagnostic survey method was used and a questionnaire was chosen as a technique. Results. The conducted analyses showed that, in the opinion of the respondents, the leading tasks of the nurses at COTUA include informing patients about the principles and methods of therapy, familiarizing them with the topography of the ward, the Charter of Patient’s Rights, the regulations of the ward, the schedule of the day and its specifics, administering medicines, providing a sense of safety, providing psychological support, transferring knowledge and learning how to live with the disease and cooperating with the therapeutic team. In addition, three quarters of the respondents indicated that the nurses working in the ward are willing to talk to patients about alcohol dependence, and a comparable percentage of the respondents assessed the effectiveness of the therapeutic methods used by the therapeutic team in relation to their own alcohol dependence problem very well and well. Conclusions. Patients’ assessment of the effectiveness of the therapeutic methods used depends on the nurses’ tasks of conducting therapeutic conversations with patients, providing them with knowledge, learning how to live with the disease, cooperating with the therapeutic team and the nurses’ readiness to talk to patients about alcohol dependence. (JNNN 2021;10(1):26–34)

Coupled Multi-Resolution WMF-FEM to Solve the Forward Problem in Magnetic Induction Tomography Technology

Magnetic Induction Tomography (MIT), is a promising modality used for non-invasive imaging. However, there are some critical limitations in the MIT technique, including the forward problem. In this study, a coupled multi-resolution method combining Wavelet-based Mech Free (WMF) method and Finite Element Method (FEM), short for WMF-FEM method, is proposed to solve the MIT forward problem. Results show that using the WMF-FEM method could successfully solve the mesh coordinates dependence problem in FEM, apply boundary condition in the WMF method, and increase MIT approximations. Simulations show improved results compared to the standard FEM and WFM method. The proposed coupled multi-resolution WMF-FEM method could be used in the MIT technique to solve the forward problem. The contribution of this paper is a simulated MIT system whose performance is closely predicted by mathematical models. The derivation of the simulation equations of the coupled WMF-FEM method is shown. This new approach to the forward problem in MIT has shown an increase in the accuracy in MIT approximations.

Recommendation Based on Users’ Long-Term and Short-Term Interests with Attention

Recommendations based on user behavior sequences are becoming more and more common. Some studies consider user behavior sequences as interests directly, ignoring the mining and representation of implicit features. However, user behaviors contain a lot of information, such as consumption habits and dynamic preferences. In order to better locate user interests, this paper proposes a Bi-GRU neural network with attention to model user’s long-term historical preferences and short-term consumption motivations. First, a Bi-GRU network is established to solve the long-term dependence problem in sequences, and attention mechanism is introduced to capture user interest changes related to the target item. Then, user’s short-term interaction trajectory based on self-attention is modeled to distinguish the importance of each potential feature. Finally, combined with long-term and short-term interests, the next behavior is predicted. We conducted extensive experiments on Amazon and MovieLens datasets. The experimental results demonstrate that the proposed model outperforms current state-of-the-art models in Recall and NDCG indicators. Especially in MovieLens dataset, compared with other RNN-based models, our proposed model improved at least 2.32% at Recall@20, which verifies the effectiveness of modeling long-term and short-term interest of users, respectively.

Normative Uncertainty and the Dependence Problem

In this paper, I enter the debate between those who hold that our normative uncertainty matters for what we ought to do, and those who hold that only our descriptive uncertainty matters. I argue that existing views in both camps have unacceptable implications in cases where our descriptive beliefs depend on our normative beliefs. I go on to propose a fix which is available only to those who hold that normative uncertainty matters, ultimately leaving the challenge as a threat to recent skepticism about such views.

Eliminative Materialism and Ordinary Language

Advocates of eliminative materialism (EM) assure us that our current, ordinary approach to describing the mind (dubbed “folk psychology”) will eventually be eliminated, instead of reduced, by a matured neuroscience. However, once we take into account the flexibility, explanatory power, and overall sophistication of ordinary language, then the promissory note offered by eliminative materialism (EM) loses all credibility. To bolster the preceding claim, we present three original problems for EM: (1) the accountability problem, (2) the substitution problem, and (3) the discourse dependence problem.

The “path dependence effect” and its application for regional studies (case of Kaliningrad oblast)

One of the main questions studying by the economic geography is the reasons for the heterogeneity of the distribution of economic processes in space. For research of this kind, it is extremely important that the researcher uses the idea of he economic process as such, the nature of its dynamics and the factors influencing its development. This paper is devoted to the concept of the “path dependence”, based on the ideas of “dependence on previous development”. The notion is clearly interdisciplinary in nature and can be used and is already used in economic and geographical research. This work is devoted to clarifying the economic and geographical content of the concept of “path dependence” and to show the demonstration of this effect in the socio-economic and spatial development of a particular region (for example, the Kaliningrad region). The paper gives review of the modern state of researches on the “path dependence” problem including main research areas. From the example of the Kaliningrad region development starting from 1945 to date the work shows both mechanism of action of the “path dependence” and mechanism of development path shift. It also describes action of “path dependence” factors and its influence on regional economic development. Apart particularities of the current development of the Kaliningrad region are characterized from the path overlocking perspective.