Stein's Theory Research Articles

Nation‐states in a Prisoner's Dilemma with climate change: Applying Edith Stein's theory of the state

AbstractTo get a better picture of the relation between nationalism and global environmental problems within the state‐dominated situation, I present the inherent logic of international environmental politics as a version of the famous Prisoner's Dilemma. I argue that the same contingent bonds that relate the members of nations to their respective nation‐states are part of the contemporary difficulty of actually working together for the common good on the international level by creating exclusive feelings of solidarity—the ‘Prisoners’ of the Dilemma. To reveal the experiential background of nation‐states in this situation, I rephrase and apply Edith Stein's theory of the state as a collective entity. Stein was an inter‐war political philosopher who is now mainly read within religious studies and philosophy of mind. As my argument implies, her work also has relevance for further affect nationalism studies.

Holomorphic functional calculus and vector-valued Littlewood–Paley–Stein theory for semigroups

We study vector-valued Littlewood–Paley–Stein theory for semigroups \{T_{t}\}_{t>0} of regular contractions on L_{p}(\Omega) for a fixed 1<p<\infty . We prove that if a Banach space X is of martingale cotype q , then there is a constant C such that \biggl\|\biggl(\int_{0}^{\infty}\biggl\|t\frac{\partial}{\partial t}P_{t} (f)\biggr\|_{X}^{q}\,\frac{dt}{t}\biggr)^{1/q}\biggr\|_{L_p(\Omega)}\le C\|f\|_{L_p(\Omega; X)}, \quad\forall f\in L_{p}(\Omega; X), where \{P_{t}\}_{t>0} is the Poisson semigroup subordinated to \{T_{t}\}_{t>0} . Let \mathsf{L}^{P}_{\mathsf{c}, q, p}(X) be the least constant C , and let \mathsf{M}_{\mathsf{c}, q}(X) be the martingale cotype q constant of X . We show \mathsf{L}^{P}_{\mathsf{c},q, p}(X)\lesssim \max(p^{1/q}, p') \mathsf{M}_{\mathsf{c},q}(X). Moreover, the order \max(p^{1/q}, p') is optimal as p\to1 and p\to\infty . If X is of martingale type q , the reverse inequality holds. If additionally \{T_{t}\}_{t>0} is analytic on L_{p}(\Omega; X) , the semigroup \{P_{t}\}_{t>0} in these results can be replaced by \{T_{t}\}_{t>0} itself. Our new approach is built on holomorphic functional calculus. Compared with the previous approaches, ours is more powerful in several aspects: (a) it permits us to go much further beyond the setting of symmetric submarkovian semigroups; (b) it yields the optimal orders of growth on p for most of the relevant constants; (c) it gives new insights into the scalar case for which our orders of the best constants in the classical Littlewood–Paley–Stein inequalities for symmetric submarkovian semigroups are better than those of Stein. In particular, we resolve a problem of Naor and Young on the optimal order of the best constant in the above inequality when X is of martingale cotype q and \{P_{t}\}_{t>0} is the classical Poisson or heat semigroup on \mathbb{R}^{d} .

Quantitative estimates for bounded holomorphic semigroups

We revisit the theory of one-parameter semigroups of linear operators on Banach spaces in order to prove quantitative bounds for bounded holomorphic semigroups. Subsequently, relying on these bounds we obtain new quantitative versions of two recent results of Xu related to the vector-valued Littlewood–Paley–Stein theory for symmetric diffusion semigroups.

Digitization and Development of Pantok Melody Themes Tongkek Using Leon Stein's Theory Approach

ABSTRACTThis paper presents a study on the composition of traditional music performance in Pancor Village, East Lombok, Indonesia with a focus on the creation of digitalized compositions based on traditional music. The study employs the approach of Leon Stein's theory of composition, which emphasizes the importance of understanding the cultural and historical context of musical works in order to create innovative and meaningful compositions.The study involves field research, where traditional music performances in Pancor Village are recorded, transcribed, and analyzed using Stein's approach to composition. The analysis focuses on identifying the characteristic elements of traditional music, such as melody, rhythm, and instrumentation, and exploring how these elements can be integrated with digital technology to create new compositions.The study also involves experimentation with digital tools, such as software synthesizers, digital audio workstations, and other music production tools, while adhering to Stein's approach to composition. These tools are used to create digitalized compositions based on the traditional music of Pancor Village, with the aim of exploring the creative possibilities of combining traditional music with modern technology, while maintaining the cultural and historical context of the original works.The results of the study show that the integration of traditional music with digital technology while employing Stein's approach to composition, can lead to the creation of innovative and compelling musical works that are relevant to contemporary audiences. The digital compositions created in this study demonstrate how traditional music can be transformed and reimagined in new and exciting ways, while still respecting the cultural and historical context of the original works.This study contributes to the ongoing conversation on the preservation and development of traditional music and demonstrates the potential of integrating traditional music with modern technology using a theoretical framework that emphasizes cultural and historical context. It also highlights the importance of understanding and respecting the cultural and historical significance of traditional music, and the role that technology can play in preserving and evolving these musical traditions.

The Limits of Simulation for Understanding Mental Illness: Defending a Steinian Theory of Empathy

AbstractI defend Edith Stein's theory of empathy as an alternative to simulation theories of empathy. Simulation theories of empathy involve using one's own cognitive resources to replicate the mental states of others by imagining being in their situation. I argue that this understanding of empathy is problematic within the context of mental healthcare because it can lead to the co-opting and assimilation of another person's experiences. In response, I maintain that Stein's theory is preferable because it involves appreciating others’ experiences as it is for them, and this alternative account of empathy avoids the assimilation of the experiences of others.

Multilinear duality and factorisation for Brascamp–Lieb-type inequalities

We initiate the study of a duality theory which applies to norm inequalities for pointwise weighted geometric means of positive operators. The theory finds its expression in terms of certain pointwise factorisation properties of function spaces which are naturally associated to the norm inequality under consideration. We relate our theory to the Maurey–Nikishin–Stein theory of factorisation of operators, and present a fully multilinear version of Maurey’s fundamental theorem on factorisation of operators through L^1 . The development of the theory involves convex optimisation and minimax theory, functional-analytic considerations concerning the dual of L^\infty , and the Yosida–Hewitt theory of finitely additive measures. We consider the connections of the theory with the theory of interpolation of operators. We discuss the ramifications of the theory in the context of concrete families of geometric inequalities, including Loomis–Whitney inequalities, Brascamp–Lieb inequalities and multilinear Kakeya inequalities.

Calderón–Zygmund operators on multiparameter Lipschitz spaces of homogeneous type

Abstract 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.

An Accidental Genre

An Accidental Genre

Trading aggressiveness and market efficiency

Stein (2009) shows that crowding by sophisticated traders can cause price overreaction. To test Stein's theory, in this paper I use trading aggressiveness after earnings releases as a measure of crowding. With a large number of traders, their strong aggregate demand makes trade execution more difficult, and leads every individual investor to trade more aggressively. I find that the prices of aggressively traded stocks overreact after good news, but not after bad news, except during the financial crisis. The asymmetry in observed results can be explained by differences in belief heterogeneity of investors and market attention during news releases.

LORENZ VON STEIN's THEORY OF WELFARE STATE AND ITS INFLUENCE ON THE PERCEPTION OF THE VALUES OF WELFARE STATE IN THE SCIENTIFIC COMMUNITY OF MODERN RUSSIA

This article analyzes the foundations of Lorenz von Stein's theory of welfare state, his views on the state, personality, society, social issue and social management. The key values of Lorenz von Stein's theory of welfare state are: statism, freedom, equality, private property, progress, social and political stability. The German scientist’s theory influences the values that determine the perception of the social state in modern Russian studies. The leading role of the state in social issue, the social responsibility of the state, the priority of freedom and personal development of the individual, the need to create equal conditions for social mobility of individuals - are the principles that are currently accepted by the scientific community when considering the nature and functions of the welfare state.

Hörmander type theorem on bi-parameter Hardy spaces for bi-parameter Fourier multipliers with optimal smoothness

The main purpose of this paper is to establish, using the bi-parameter Littlewood–Paley–Stein theory (in particular, the bi-parameter Littlewood–Paley–Stein square functions), a Hörmander–Mihlin type theorem for the following bi-parameter Fourier multipliers on bi-parameter Hardy spaces H^p(\mathbb{R}^{n_1}\!\times \mathbb{R}^{n_2}) ( 0 < p\le 1 ) with optimal smoothness: T_mf(x_1, x_2)=\frac{1}{(2\pi)^{n_1+n_2}}\int_{\mathbb{R}^n\times \mathbb{R}^m}m(\xi, \eta)\hat{f}(\xi, \eta)e^{2\pi(x_1\xi+x_2\eta)}\,d\xi \,d\eta. One of our results (Theorem 1.7) is the following: assume that m(\xi,\eta) is a function on \mathbb{R}^{n_1}\!\times \mathbb{R}^{n_1} satisfying \sup_{j,k\in \mathbb{Z}}\|m_{j,k}\|_{W^{(s_1,s_2)}}<\infty, with s_1 > n_1({1}/{p}-{1}/{2}) , s_2 > n_2({1}/{p}-{1}/{2}) . Then T_m is bounded from H^p(\mathbb{R}^{n_1}\!\times \mathbb{R}^{n_2}) to H^p(\mathbb{R}^{n_1}\!\times \mathbb{R}^{n_2}) for all 0 < p\le 1 , and \|T_m\|_{H^p\rightarrow H^p}\lesssim \sup_{j,k\in \mathbb{Z}}\|m_{j,k}\|_{W^{(s_1,s_2)}}. Moreover, the smoothness assumption on s_1 and s_2 is optimal. Here, m_{j,k}(\xi,\eta)=m(2^j\xi,2^k\eta)\Psi(\xi)\Psi(\eta) , where \Psi(\xi) and \Psi(\eta) are suitable cut-off functions on \mathbb{R}^{n_1} and \mathbb{R}^{n_2} , respectively, and W^{(s_1, s_2)} is a two-parameter Sobolev space on \mathbb{R}^{n_1}\!\times \mathbb{R}^{n_2} . We also establish that under the same smoothness assumption on the multiplier m , \|T_m\|_{H^p\rightarrow L^p}\!\lesssim\! \sup_{j,k\in \mathbb{Z}}\|m_{j,k}\|_{W^{(s_1,s_2)}} and \|T_m\|_{{\rm CMO}_p\rightarrow {\rm {CMO}}_p}\lesssim \sup_{j,k\in \mathbb{Z}}\|m_{j,k}\|_{W^{(s_1,s_2)}} for all 0 < p\le 1 . Moreover, \|T_m\|_{L^p\rightarrow L^p}\lesssim \sup_{j,k\in \mathbb{Z}}\|m_{j,k}\|_{W^{(s_1,s_2)}} for all 1 < p < \infty under the assumption s_1 > n_1/2 and s_2 > n_2/2 .

Atomic Decompositions of Localized Hardy Spaces with Variable Exponents and Applications

In this paper, we introduce the localized Hardy spaces with variable exponents $$h^{p(\cdot )}$$ and establish a new atomic decomposition theorem for $$h^{p(\cdot )}$$ by using the discrete Littlewood–Paley–Stein theory. As an application of atomic decomposition, we investigate molecule decomposition for $$h^{p(\cdot )}$$ . Moreover, pseudo-differential operators of order zero are shown to be bounded on $$h^{p(\cdot )}$$ .

Atomic decomposition of variable Hardy spaces via Littlewood–Paley–Stein theory

The purpose of this paper is to give a new atomic decomposition for variable Hardy spaces via the discrete Littlewood–Paley–Stein theory. As an application of this decomposition, we assume that T is a linear operator bounded on Lq and Hp(⋅), and we thus obtain that T can be extended to a bounded operator from Hp(⋅) to Lp(⋅).

Two-loop renormalization of the Finkel’stein theory: The specific heat

We explore the two-loop renormalization of the specific heat for an interacting disordered electron system in the case of broken time reversal symmetry. Within the nonlinear sigma model approach we derive the two-loop result for the anomalous dimension which controls scaling of the specific heat with temperature. As an example, we elaborate the metal–insulator transition in d=2+ϵ dimensions for the case of broken time reversal and spin rotational symmetries and in the presence of Coulomb interaction. In this situation scaling of the specific heat is determined by the anomalous dimension of the Finkel’stein operator which is the eigenoperator of the renormalization group complementary to the eigenoperator corresponding to the second moment of the local density of states. We find that the absolute values of the anomalous dimensions of these operators differ beyond one-loop approximation contrary to the noninteracting case.

Planck’s Quantum Hypothesis and Concept of Mass from Special Relativity

It is established that special relativity and quantum mechanics are two very wide apart theories of measurements in modern physics in terms of determinism versus indeterminism. Modern physics accepts indeterminism against classical determinism. But it is remarkable that Einstein's special relativity in its present form alone contains the basic ingredients of quantum theory. Einstein's theory can give a simple theoretical proof of the Planck's quantum hypothesis and can explain the origin of mass out of zero rest mass of photon. This article at the first place shows how to proceed in this path from relativistic energy momentum relations and at the second place it shows the reason of energy and momentum indeterminacy from the framework of relativity. At the last phase the article puts a question on the sustainability of special relativity itself before oscillation of any kind. This paper deals with the matter to the extent special relativity containing quantum theory. Index Terms— Special relativity, simultaneity of events, Planck's quantum theory, energy momentum 4 vector, Heisenberg's indeterminacy principle, concept of mass, ensemble of photon. —————————— a —————————— 1 I NTRODUCTION t is a common belief that the jurisdiction of special relativi- ty and quantum theory are mutually exclusive. In 1900 Max Planck gave his famous quantum hypothesis of light together with the energy- frequency relation . Eh Q In 1905 Einstein gave special relativity. Both the regime went their own way and ultimately clashed each other with the arrival of Heisenberg's indeterminacy principle in 1926. Einstein con- ceded defeat to Bohr ultimately but still believed that quan- tum theory lacks something very serious. But modern physics points clearly to the triumph of Heisenberg's indeterminacy principle in every context. Nonetheless it is worthwhile to mention that the very genesis of quantum theory of light pre- scribed by Eh Q and the very essence of mass can be de- rived even in the frame work of special relativity. Even Ein- stein could get it using his own energy momentum relation. Planck's quantum relation of photon and the construction of mass from an ensemble of photons are indeed inbuilt in Ein- stein's theory. We can even reconcile Heisenberg's principle of indeterminacy with the framework built by Einstein.

Break-up of bubble clusters in turbulent flow—Theory

The behaviour of bubble clusters in turbulent conditions has been studied theoretically. The cluster behaviour was modelled based on concept drawn from the related field of bubble breakup. It was assumed that the bubbles were bridged by particles, so the cohesive strength was determined by the capillary force between the bubbles and the particles. Two different theories were investigated for the disruptive force from the turbulent liquid: the shear rate hypothesis of Camp and Stein (1943), and the turbulent fluctuation model arising from Kolmogorov's theory of isotropic turbulence (Kolmogorov, 1941). It was found that neither method is applicable in the fragmentation stage. However, in the equilibrium stage, an equation derived from Camp and Stein's theory was more realistic than that obtained using Kolmogorov's equation.

Estimates for vector-valued holomorphic functions and Littlewood–Paley–Stein theory

In this paper we consider generalized square function norms of holomorphic functions with values in a Banach space. One of the main results is a characterization of embeddings of the form \[L^p(X)\subseteq \gamma(X) \subseteq L^q(X),\] in terms of the type $p$ and cotype $q$ for the Banach space $X$. As an application we prove $L^p$-estimates for vector-valued Littlewood-Paley-Stein $g$-functions and derive an embedding result for real and complex interpolation spaces under type and cotype conditions.

Fractional vector-valued Littlewood–Paley–Stein theory for semigroups

We consider the fractional derivative of a general Poisson semigroup. With this fractional derivative, we define the generalized fractional Littlewood–Paley g-function for semigroups acting on Lp-spaces of functions with values in Banach spaces. We give a characterization of the classes of Banach spaces for which the fractional Littlewood–Paley g-function is bounded on Lp-spaces. We show that the class of Banach spaces is independent of the order of derivation and coincides with the classical (Lusin-type/-cotype) case. We also show that the same kind of results exist for the case of the fractional area function and the fractional gλ*-function on ℝn. Finally, we consider the relationship of the almost sure finiteness of the fractional Littlewood–Paley g-function, the area function and the gλ*-function with the Lusin-cotype property of the underlying Banach space. As a byproduct of the techniques developed, one can find some results of independent interest for vector-valued Calderón–Zygmund operators. For example, one can find the following characterization: a Banach space is the unconditional martingale difference if and only if, for some (or, equivalently, for every) p ∈ [1, ∞), dy exists for almost every x ∈ ℝ and every .

Smooth embeddings with Stein surface images

A simple characterization is given of open subsets of a complex surface that smoothly perturb to Stein open subsets. As applications, ℂ2 contains domains of holomorphy (Stein open subsets) that are exotic smoothings of ℝ4, and others homotopy equivalent to S2 but cut out by smooth, compact 3-manifolds. Pseudoconvex embeddings of Brieskorn spheres and other 3-manifolds into complex surfaces are constructed, as are pseudoconcave holomorphic fillings (with disagreeing contact and boundary orientations). Pseudoconcave complex structures on Milnor fibers are found. A byproduct of this construction is a simple polynomial expression for the signature of the (p, q, npq−1) Milnor fiber. Akbulut corks in complex surfaces can always be chosen to be pseudoconvex or pseudoconcave submanifolds. The main theorem is expressed via Stein handlebodies (possibly infinite), which are defined holomorphically in all dimensions by extending Stein theory to manifolds with non-compact boundary.

Theory implementation: Stein's theory of meaning through cognitive-behavioural process: a pilot study

This theory development was a partial fulfilment of doctoral course work at University of Colorado Denver Health Sciences Center. It is an interactive/integrated theory which can be utilized in multiple practice settings to promote growth of the client as well as the nurse. Tools were developed pertaining to this theory. A pilot study was accomplished at a local mental health centre.