On the extremal solutions of superlinear Helmholtz problems

In this note, we deal with the Helmholtz equation −∆u+cu = λf(u) with Dirichlet boundary condition in a smooth bounded domain Ω of R n , n > 1. The nonlinearity is superlinear that is limt−→∞ f(t) t = ∞ and f is a positive, convexe and C 2 function defined on [0,∞). We establish existence of regular solutions for λ small enough and the bifurcation phenomena. We prove the existence of critical value λ ∗ such that the problem does not have solution for λ > λ∗ even in the weak sense. We also prove the existence of a type of stable solutions u ∗ called extremal solutions. We prove that for f(t) = e t , Ω = B1 and n ≤ 9, u ∗ is regular.

Can you sign a quantum state?

Cryptography with quantum states exhibits a number of surprising and counterintuitive features. In a 2002 work, Barnum et al. argue that these features imply that digital signatures for quantum states are impossible (Barnum et al., FOCS 2002). In this work, we ask: can all forms of signing quantum data, even in a possibly weak sense, be completely ruled out? We give two results which shed significant light on this basic question.First, we prove an impossibility result for digital signatures for quantum data, which extends the result of Barnum et al. Specifically, we show that no nontrivial combination of correctness and security requirements can be fulfilled, beyond what is achievable simply by measuring the quantum message and then signing the outcome. In other words, only classical signature schemes exist.We then show a positive result: a quantum state can be signed with the same security guarantees as classically, provided that it is also encrypted with the public key of the intended recipient. Following classical nomenclature, we call this notion quantum signcryption. Classically, signcryption is only interesting if it provides superior performance to encypt-then-sign. Quantumly, it is far more interesting: it is the only signing method available. We develop "as-strong-as-classical" security definitions for quantum signcryption and give secure constructions based on post-quantum public-key primitives. Along the way, we show that a natural hybrid method of combining classical and quantum schemes can be used to "upgrade" a secure classical scheme to the fully-quantum setting, in a wide range of cryptographic settings including signcryption, authenticated encryption, and CCA security.

Wildcat or Lion? Inequality, Agency, and the New Chinese Working Class

<p>The study of Chinese labour politics has returned to the centre of scholarly interest as China has increasingly become involved in global production and trade. As the incidence of labour dispute and workers’ strikes continued to soar, ubiquitous cases of labour rights abuse have been widely reported by international media and academics. The literature of Marxist international political economy has long predicted the insurgency of the Chinese working class resulting from rising inequality, global capital movement and labour division. In contrast, traditional Chinese labour studies are inconclusive as to whether the Chinese working class has gained enough class consciousness to become a cohesive agent for social and political change. This research examines how rising economic, social and political inequalities have impacted on the Chinese working class’s agency. The research shifts the focus from top-down structural analysis to workers’ agency itself, with an emphasis on their cognitive strength. The research was undertaken via a two-case comparative study of the Chinese working class in four megacities and four smaller cities. Data came mostly from statistics and field interviews. This two-case comparative study concludes that, overall, the Chinese working class had a weak behavioural strength, as manifested by inconsistent wildcat-style strikes, which had no clear political strategies. This research also concludes that the working class’s cognitive agency is weak and conservative, as manifested by a weak class identification, their poor understanding of democracy, their low willingness to participate in collective action, and their weak sense of class solidarity. I argue that inequalities and capital movement do not have a simple and unidirectional relationship with the working class’s collective agency. On the one hand, inequalities and capital movement can arouse the working class’s behavioural strength quickly. On the other hand, workers’ cognitive strength is more inert and does not correspond neatly to these two factors. The research findings show that the megacities are more economically developed, with higher inequalities, but with considerably weaker and more conservative working class agency; whereas the smaller cities are less economically developed, with lower inequalities, but with less weak and conservative working class agency. The addition of cognitive strength as a new dimension of working class study provides a pluralist analytical framework for the study of Chinese labour. The new Chinese working class are better educated and more individualised with three main characteristics - occupation-based, precarious, and conservative - which distinguish them from the older generations of workers who had a clear group identification, such as the SOE workers in the 1990s, and the rural migrant workers in the 2000s. These theoretical and empirical findings open up possibilities of new strategies for effective labour organisation that should be considered by labour NGOs, civil society and the government. These players not only need to manage the working class action carefully, but also need to better understand the workers’ complex cognitive situations.</p>

Wildcat or Lion? Inequality, Agency, and the New Chinese Working Class

<p>The study of Chinese labour politics has returned to the centre of scholarly interest as China has increasingly become involved in global production and trade. As the incidence of labour dispute and workers’ strikes continued to soar, ubiquitous cases of labour rights abuse have been widely reported by international media and academics. The literature of Marxist international political economy has long predicted the insurgency of the Chinese working class resulting from rising inequality, global capital movement and labour division. In contrast, traditional Chinese labour studies are inconclusive as to whether the Chinese working class has gained enough class consciousness to become a cohesive agent for social and political change. This research examines how rising economic, social and political inequalities have impacted on the Chinese working class’s agency. The research shifts the focus from top-down structural analysis to workers’ agency itself, with an emphasis on their cognitive strength. The research was undertaken via a two-case comparative study of the Chinese working class in four megacities and four smaller cities. Data came mostly from statistics and field interviews. This two-case comparative study concludes that, overall, the Chinese working class had a weak behavioural strength, as manifested by inconsistent wildcat-style strikes, which had no clear political strategies. This research also concludes that the working class’s cognitive agency is weak and conservative, as manifested by a weak class identification, their poor understanding of democracy, their low willingness to participate in collective action, and their weak sense of class solidarity. I argue that inequalities and capital movement do not have a simple and unidirectional relationship with the working class’s collective agency. On the one hand, inequalities and capital movement can arouse the working class’s behavioural strength quickly. On the other hand, workers’ cognitive strength is more inert and does not correspond neatly to these two factors. The research findings show that the megacities are more economically developed, with higher inequalities, but with considerably weaker and more conservative working class agency; whereas the smaller cities are less economically developed, with lower inequalities, but with less weak and conservative working class agency. The addition of cognitive strength as a new dimension of working class study provides a pluralist analytical framework for the study of Chinese labour. The new Chinese working class are better educated and more individualised with three main characteristics - occupation-based, precarious, and conservative - which distinguish them from the older generations of workers who had a clear group identification, such as the SOE workers in the 1990s, and the rural migrant workers in the 2000s. These theoretical and empirical findings open up possibilities of new strategies for effective labour organisation that should be considered by labour NGOs, civil society and the government. These players not only need to manage the working class action carefully, but also need to better understand the workers’ complex cognitive situations.</p>

Calderón–Zygmund operators on multiparameter Lipschitz spaces of homogeneous type

The purpose of this paper is to establish a necessary and sufficient condition for the boundedness of general product singular integral operators introduced by Han, Li and Lin [Y. Han, J. Li and C.-C. Lin, Criterion of the L 2 L^{2} boundedness and sharp endpoint estimates for singular integral operators on product spaces of homogeneous type, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 16 2016, 3, 845–907] on the multiparameter Lipschitz spaces of homogeneous type M ~ = M 1 × ⋯ × M n {\tilde{M}=M_{1}\times\cdots\times M_{n}} . Each factor space M i {M_{i}} , 1 ≤ i ≤ n {1\leq i\leq n} , is a space of homogeneous type in the sense of Coifman and Weiss. These operators generalize those studied by Journé on the Euclidean space and include operators studied by Nagel and Stein on Carnot–Carathéodory spaces. The main tool used here is the discrete Littlewood–Paley–Stein theory and almost orthogonality together with a density argument for the product Lipschitz spaces in the weak sense.

Convergence of nonlinear numerical approximations for an elliptic linear problem with irregular data

This work is devoted to the study of the approximation, using two nonlinear numerical methods, of a linear elliptic problem with measure data and heterogeneous anisotropic diffusion matrix. Both methods show convergence properties to a continuous solution of the problem in a weak sense, through the change of variable u = ψ(v), where ψ is a well chosen diffeomorphism between (−1, 1) and R, and v is valued in (−1, 1). We first study a nonlinear finite element approximation on any simplicial grid. We prove the existence of a discrete solution, and, under standard regularity conditions, we prove its convergence to a weak solution of the problem by applying Hölder and Sobolev inequalities. Some numerical results, in 2D and 3D cases where the solution does not belong to H 1(Ω), show that this method can provide accurate results. We then construct a numerical scheme which presents a convergence property to the entropy weak solution of the problem in the case where the right-hand side belongs to L1 . This is achieved owing to a nonlinear control volume finite element (CVFE) method, keeping the same nonlinear reformulation, and adding an upstream weighting evaluation and a nonlinear p−Laplace vanishing stabilisation term.

A Large Sample Survey of Suicide Risk among University Students in China

Background This study aimed to examine suicide ideation, suicide attempts, and suicide risk by examining a large sample of Chinese university students and identify the predictive factors, including depressive and anxiety symptoms, for suicide attempt and suicide risk. Methods We recruited 6,836 students (aged 18–30) based on all students enrolled in 2016 from one university using cluster sampling. They completed four questionnaires: the Beck Scale for Suicide Ideation and the Suicidal Behaviors Questionnaire-Revised were used to measure suicide risk, and students’ depressive/anxiety symptoms were estimated using Patient Health Questionnaire and Generalized Anxiety Disorder Scale. Results Four major findings emerged. First, 18% of the students showed high suicide ideation, 14.5% showed suicide risk, 18.8% had suicide plans, and 1% had attempted suicide. Second, a weak sense of life’s value was common among university students, as 61.4% of students considered suicide as a way to end or evade problems. Third, the results of the binary logistic regression showed that education, suicide ideation, including the wish to die, attitude toward suicide, specificity/planning of suicide, and deception or concealment of contemplated suicide were predictive factors of suicide attempt and suicide risk. The variable “deterrents to active attempt” was also a predictive factor of suicide risk. Fourth, depressive and anxiety symptoms did not significantly predict suicide attempts or suicide risk. Only 10.8% and 5.6% of the students had self-reported scores above the clinical cut-off points for depression and anxiety, respectively. Conclusions This study highlighted the prevalence of suicide risk among Chinese university students. The high risk of suicide may not only be due to affective disorders, but also a weak sense of life’s value or other reasons. Suicide ideation that significantly predicts suicide risk can be used for suicide risk assessment. Universities should provide appropriate life education and suicide prevention and intervention such as teaching instructors gate-keeper skills.

Serre–Tate theory for Calabi–Yau varieties

Classical Serre–Tate theory describes deformations of ordinary abelian varieties. It implies that every such variety has a canonical lift to characteristic zero and equips the base of its universal deformation with a Frobenius lifting and canonical multiplicative coordinates. A variant of this theory has been obtained for ordinary K3 surfaces by Nygaard and Ogus. In this paper, we construct canonical liftings modulo p 2 {p^{2}} of varieties with trivial canonical class which are ordinary in the weak sense that the Frobenius acts bijectively on the top cohomology of the structure sheaf. Consequently, we obtain a Frobenius lifting on the moduli space of such varieties. The quite explicit construction uses Frobenius splittings and a relative version of Witt vectors of length two. If the variety has unobstructed deformations and bijective first higher Hasse–Witt operation, the Frobenius lifting gives rise to canonical coordinates. One of the key features of our liftings is that the crystalline Frobenius preserves the Hodge filtration. We also extend Nygaard’s approach from K3 surfaces to higher dimensions, and show that no non-trivial families of such varieties exist over simply connected bases with no global one-forms.

Wherein is the concept of disease normative? From weak normativity to value-conscious naturalism

In this paper we focus on some new normativist positions and compare them with traditional ones. In so doing, we claim that if normative judgments are involved in determining whether a condition is a disease only in the sense identified by new normativisms, then disease is normative only in a weak sense, which must be distinguished from the strong sense advocated by traditional normativisms. Specifically, we argue that weak and strong normativity are different to the point that one ‘normativist’ label ceases to be appropriate for the whole range of positions. If values and norms are not explicit components of the concept of disease, but only intervene in other explanatory roles, then the concept of disease is no more value-laden than many other scientific concepts, or even any other scientific concept. We call the newly identified position “value-conscious naturalism” about disease, and point to some of its theoretical and practical advantages.

A mortar formulation for frictionless line-to-line beam contact

This paper describes the quasi-static formulation of frictionless line contact between flexible beams by employing the mortar finite element approach. Contact constraints are enforced in a weak sense along the contact region using Lagrange multipliers. A simple projection appropriate for thin beams with circular cross-sections is proposed for the computation of contact regions. It is combined with the geometrically exact beam formalism on the Lie group $SE(3)$ S E ( 3 ) . Interestingly, this framework leads to a constraint gradient and a tangent stiffness invariant under rigid body transformations. The formulation is tested in some numerical examples.