An algebraic approach to the study of entanglement entropy of quantum systems is reviewed. Starting with a state on a \(C^*\)-algebra, one can construct a density operator describing the state in the ...GNS representation state. Applications of this approach to the study of entanglement measures for systems of identical particles are outlined. The ambiguities in the definition of entropy within this approach are then related to the action of unitaries in the commutant of the representation and their relation to modular theory explained.
An approach to renormalization of scalar fields on the Doplicher-Fredenhagen-Roberts (DFR) quantum spacetime is presented. The effective non-local theory obtained through the use of states of optimal ...localization for the quantum spacetime is reformulated in the language of (perturbative) Algebraic Quantum Field Theory. The structure of the singularities associated to the non-local kernel that codifies the effects of noncommutativity is analyzed using the tools of microlocal analysis.
The new 2-amino-3- R -4-aryl-6-ethyl-4,6-dihydropyrano3,2- c 2,1benzothiazine 5,5-dioxides were synthesized via three-component interaction of 1 H -2,1-benzothiazin-4(3 H )-one 2,2-dioxide with ...arylcarbaldehydes and active methylene nitriles. Depending on the nature of an active methylene nitrile and an arylcarbaldehyde this interaction can lead either to the target 2-amino-4 H -pyrans or to the stable triethylammonium salts of bis(1 H -2,1-benzothiazin-4(3 H )-one 2,2-dioxides) (bis-adducts). The latter is a completely new product of such interaction. The structure of the bis-adduct was confirmed by single crystal X-ray diffraction. Actually, the formation of stable triethylammonium salts (as the process competitive with the 2-amino-4 H -pyrans formation) appeared to be reversible and their interaction with active methylene nitriles led to the formation of 2-amino-4 H -pyrans. The extended and adjusted mechanism of the three-component interaction, that includes the bis-adducts formation stage, was proposed. Taking into account the peculiarities of the mechanism, we were capable to control the reaction selectivity.
The interaction employing sulfamide and enolizable ketones was closely inspected in Biginelli reaction. The three-component variation of the reaction ''sulfamide + ketone + anisaldehyde'' and ...''sulfamide + ketone +
N
,
N
-diethylacetoacetamide'' featured a lack of selectivity and provided a mixture of possible condensation products. Selectivity was improved when ketones were used in the reaction both as carbonyl and enol components. It was shown that trimethylsilyl chloride promoted interaction of sulfamide with ketones to afford 1,2,6- thiadiazines. Limitations were noted and unpredictable outcomes of the reaction were discussed as well.
The article highlights the challenges and opportunities in the development of the piperazine-fused triazoles. Approaches toward medicinal chemistry relevant building blocks based on 1,2,4triazolo4,3-
...a
pyrazine platform were elaborated. The methods provide quick and multigram access to the target derivatives starting from commercially available nonexpensive reagents. The approaches were used to create a small library of the triazolopyrazines with variety of substituents in position 3. The potential of further synthetic application of the library members for medicinally oriented synthesis was shown.
The reactivity of 1,2-benzoxathiin-4(3
)-one 2,2-dioxide was studied in multicomponent type reactions for the first time, namely, in a three-component interaction with active methylene nitriles and ...aromatic aldehydes in order to construct condensed 2-amino-4
-pyran derivatives. The reaction outcome strongly depended on the nature of an active methylene nitrile and an arenecarbaldehyde. Application of malononitrile resulted in novel 2-amino-4-aryl-4
-pyrano3,2-
1,2benzoxathiine-3-carbonitrile 5,5-dioxides in most cases, whereas the utilization of ethyl cyanoacetate resulted in a complex mixture of products. In the last case, three different products were isolated depending on the arenecarbaldehyde used, namely ethyl 2-amino-4-aryl-4
-pyrano3,2-
1,2benzoxathiine-3-carboxylate 5,5-dioxides, ethyl 2-cyano-3-arylacrylates, and salts of 3,3'-(arylmethylene)bis(4-hydroxybenzo
1,2oxathiine 2,2-dioxides). Attempts to obtain separately ethyl 2-amino-4-aryl-4
-pyrano3,2-
1,2benzoxathiine-3-carboxylate 5,5-dioxides enabled us to propose reaction pathways leading to these products. The salts were obtained for the first time. The preparative method for the synthesis of triethylammonium salts of 3,3'-(arylmethylene)bis(4-hydroxybenzo
1,2oxathiine 2,2-dioxides) was proposed by the direct interaction of 1,2-benzoxathiin-4(3
)-one 2,2-dioxide with arenecarbaldehydes. The application of ammonium acetate as a catalyst allowed us to synthesize 7-aryl-7,14-dihydrobenzo5,61,2oxathiino4,3-
benzo5,61,2oxathiino3,4-
pyridine 6,6,8,8-tetraoxides containing a novel heterocyclic system. These facts, combined with our past investigations, allowed us to assert that the reactivity of enol nucleophiles that include the COCH
SO
X fragment has not been reported previously.
Spiro(2-amino-3-R-6-ethyl-4,6-dihydropyrano3,2-c2,1benzothiazine-5,5-dioxide)-4,3′-(1′-R′-5′-R″-indolin-2′-one) compounds were synthesized based on the three-component interaction of ...benzoc2,1thiazin-4-on 2,2-dioxide with corresponding isatins and appropriate methylene active nitriles in the presence of a base as a catalyst. The molecular structures of the target compounds were proved uniquely by the X-ray diffraction analysis method.
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The development of medicines with several pharmacological activities, including the analgesic, anti-inflammatory and antimicrobial properties, is one of the challenging tasks of modern medicinal ...chemistry. Aim. To expand the range of novel spiro-condensed derivatives of 1,2-benzoxathiin-4(3H)-one 2,2-dioxide, and study the biological activity of the substances obtained. Results and discussions. The target compounds were synthesized as a result of the interaction of 1,2-benzoxathiin-4(3H)-one 2,2-dioxide, malononitrile and isatins. When using ethyl cyanoacetate the interaction appeared to be much more complicated and requires further research. The study of the biological activity has revealed the compounds with the analgesic properties and the antimicrobial effect against gram-positive strains. Experimental part. Two new 2-amino-2’-oxospiro4H-pyrano3,2-c1,2benzoxathiine-4,3’-indoline-3-carbonitrile 5,5-dioxides were synthesized by the three-component reaction based on 1,2-benzoxathiin-4(3H)-one 2,2-dioxide. The anti-inflammatory activity was studied on the model of the carrageenan induced paw edema, and the analgesic activity was assessed on the model of the local inflammatory hyperalgesia. The study of the antimicrobial activity of the compounds obtained was performed by the agar well diffusion method. Conclusions. New spirobenzoеpyrano3,2-c1,2oxathiin-4,3’-indolil-3-carbonitrile 5,5-dioxides have been synthesized. The compounds obtained have revealed high levels of the analgesic properties and the antimicrobial activity. The latter exceeds the activity of the reference drugs, and has appeared to be higher against grampositive bacteria.
A questionnaire survey was undertaken to assess the impact of a nationwide educational campaign about epilepsy on the knowledge and attitudes toward the disease among Italian primary school teachers. ...Five hundred and eighty-two teachers participated. All interviewees were aware of the existence of epilepsy, and most of them had direct experience with the disease. Answers about frequency, causes, outcome, and response to treatments were variable and not correlated with age, residency, and years of experience. Teachers had positive attitudes toward epilepsy, except for the idea that driving and sports can be safe for people with epilepsy. Epilepsy and its treatment were considered a source of learning disability and social disadvantages. Several teachers declared themselves being unable to help a child having seizures. Calling an ambulance was a frequent action. Knowledge and attitudes toward epilepsy are improved compared with those reported in our previous studies. Although this may be a positive reflection of the increasing knowledge and the greater availability of information on epilepsy, there are still areas of uncertainty and incorrect behaviors.
4,6-Dihydropyrano3,2-
c
2,1benzothiazine 5,5-dioxides were synthesized
via
three-component interaction of 1-ethyl-1
H
-2,1-benzothiazin-4(3
H
)-one 2,2-dioxide with active methylene nitriles and ...cycloalkanecarbaldehydes. The latter were also applied to obtain ammonium salts of 3,3'-(cycloalkylmethanediyl)bis(1-ethyl-1
H
-2,1-benzothiazin-4-ol) 2,2,2',2'-tetraoxides. The structures of the synthesized compounds were confirmed by
1
H,
13
C NMR as well as mass spectral and elemental analysis data. The structures of two representatives from each class of the target compounds have been additionally confirmed by single crystal X-ray diffraction study. The synthesized compounds were screened for antibacterial and antifungal activities.
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![Spiro[benzo[е]pyrano[3,2-c]...](http://api.summon.serialssolutions.com/2.0.0/image/issn/XR4PS5YY4K/2308-8303_2518-1548/small "Spiro[benzo[е]pyrano[3,2-c][1,2]oxathiin-4,3’-indolil]-3-carbonitrile 5,5-dioxides: synthesis and the biological activity study")
