A general Trotter-Kato formula for a class of evolution operators

In this article we prove new results concerning the existence and various properties of an evolution system U(A+B)(t, s)0 <= s <= t <= T generated by the sum -(A(t) + B(t)) of two linear, time-dependent, and generally unbounded operators defined on time-dependent domains in a complex and separable Banach space B. In particular, writing L(B) for the algebra of all linear bounded operators on B, we can express U(A+B)(t, s)0 <= s <= t <= T as the strong limit in C(8) of a product of the holomorphic contraction semigroups generated by -A (t) and - B(t), respectively, thereby proving a product formula of the Trotter-Kato type under very general conditions which allow the domain D(A(t) + B(t)) to evolve with time provided there exists a fixed set D subset of boolean AND(t is an element of)[0,T] D(A(t) + B(t)) everywhere dense in B. We obtain a special case of our formula when B(t) = 0, which, in effect, allows us to reconstruct U(A)(t, s)0 <=(s)<=(t)<=(T) very simply in terms of the semigroup generated by -A(t). We then illustrate our results by considering various examples of nonautonomous parabolic initial-boundary value problems, including one related to the theory of timedependent singular perturbations of self-adjoint operators. We finally mention what we think remains an open problem for the corresponding equations of Schrodinger type in quantum mechanics.

A Trotter-Kato product formula for a class of non-autonomous evolution equations

In this article dedicated to Professor V. Lakshmikantham on the occasion of the celebration of his 84th birthday, we announce new results concerning the existence and various properties of an evolution system UA+B(t, s)(0 <= s <= t <= T) generated by the sum -(A(t)+B(t)) of two linear, time-dependent and generally unbounded operators defined on time-dependent domains in a complex and separable Banach space B. In particular, writing G(B) for the algebra of all linear bounded operators on B, we can express UA+B(t, s)(0 <= s <= t <= T) as the strong limit in L(B) of a product of the holomorphic contraction semigroups generated by -A(t) and -B(t), thereby getting a product formula of the Trotter-Kato type under very general conditions which allow the domain D(A(t)+B(t)) to evolve with time provided there exists a fixed set D subset of boolean AND D-t epsilon[0,D-T](A(t)+B(t)) everywhere dense in B. We then mention several possible applications of our product formula to various classes of non-autonomous parabolic initial-boundary value problems, as well as to evolution problems of Schrodinger type related to the theory of time-dependent singular perturbations of self-adjoint operators in quantum mechanics. We defer all the proofs and all the details of the applications to a separate publication. (C) 2008 Elsevier Ltd. All rights reserved.

Neolignans and sesquiterpenes from leaves and embryogenic cultures of Ocotea Catharinensis (Lauraceae)

The extracts from leaves of Ocotea catharinensis Mez (Lauraceae) were found to contain fourteen neolignans and two sesquiterpenes: nine benzofuran types (including three new compounds 1e, 2f and 4b), one new seco-benzofuran type (3b), two bicyclo[3.2.1]octane types (including the new compound 5c), two new dimers of bicyclo[3.2.1]octane type (7a and 7b) and two sesquiterpenes (including a new humulanol 9). In addition, seven neolignans were also showed to occur in somatic embryos of O. catharinensis including one new bicyclo[3.2.1]octane type (4a).

Insect feeding preferences on Piperaceae species observed in São Paulo city, Brazil

Piperaceae species have been placed among the basal angiosperm and are adapted to a variety of habitats including moist forests, secondary vegetation and dry high lands. The major anatomical/morphology features are of small trees, vines, and shrubs for Piper species, while the epiphytic and succulent characteristics are predominant forms among Peperomia species. Their secondary chemistry can be mostly represented by amides, phenylpropanoids/lignoids, and chromenes in addition to a phletoria of biosynthetically mixed-origin secondary compounds. Although several amides and lignans are known as insecticides, several phytophagous insects, among which some considered pests of economic importance, have been observed feeding vigorously on Piperaceae species. Herein we describe the feeding preferences of fourteen phytophagous species of Coleoptera, Lepidoptera and Hemiptera over approximately fifty Piperaceae species observed in São Paulo, SP, Brazil, in a long-term basis.

Flavonas, lignanas e terpeno de Piper umbellata (Piperaceae)

The phytochemical investigation of Piper umbellata leaves yielded nine compounds including one terpenoid glucoside, five flavones (vitexin 2"-O-β-glucopyranoside, apigenin 8-C-β-D-glucopyranoside,orientin 8-C-β-D-glucopyranoside,5-hydroxy-7,3',4'-trimethoxy-flavone and velutin), two lignans (sesamin e dihydrocubebin) and 4-nerolidylcathecol. Excepting 4-nerolidylcathecol, all compounds have not been described from this species yet.

Trypanocidal activity of Piper arboreum and Piper tuberculatum (Piperaceae)

In the scope of our ongoing research on bioactive agents from Brazilian flora, twenty-four extracts and fractions obtained from Piper arboreum Aub. and Piper tuberculatum Jacq. (Piperaceae) were screened for trypanocidal activity by using MTT colorimetric assay. The strongest activity was found in hexane fractions from the leaves of P. arboreum (IC50= 13.3 µg/ mL) and P. tuberculatum (IC50 = 17.2 µg/mL). Hexane fractions of the fruits of P. tuberculatum and P. arboreum showed potent toxic effects on epimastigote forms of Trypanosoma cruzi, with values of IC50 (µg/mL) of 32.2 and 31.3, respectively. Additionally, the phytochemical study of the hexane fraction of P. arboreum leaves furnished two pyrrolidine amides, piperyline (1) and 4,5-dihydropiperyline (2), which could be responsible, at least in part for the observed antiprotozoal activity.

Hydrolysis of methyl benzoate from Piper arboreum by Naupactus bipes beetle

A new natural product was isolated from Piper arboreum (Piperaceae) leaves, the methyl 3-geranyl-4-hydroxybenzoate (1). The metabolism of P. arboreum leaves by Naupactus bipes beetle (Germar, 1824 - Coleoptera: Curculionidae) led to the hydrolysis of 1 to 3-geranyl-4-hydroxybenzoic acid (2). The structures of both compounds were determined based on spectroscopic analysis (¹H and 13C NMR, MS, and IR).

Low-Level Laser Therapy in Burning Mouth Syndrome Patients: A Pilot Study

Objective: The aim of this study was to investigate the effect of low-level laser therapy (LLLT) on the treatment of burning mouth syndrome (BMS). In addition, the laser effect was compared on the different affected oral sites. Materials and Methods: Eleven subjects with a total of 25 sites (tongue, lower lip, upper lip, and palate) affected by a burning sensation were selected. The affected areas were irradiated once a week for three consecutive weeks with an infrared laser (lambda = 790 nm). The probe was kept in contact with the tissue, and the mucosal surface was scanned during the irradiation. The exposure time was calculated based on the fluence of 6 J/cm(2), the output power of 120 mW, and the area to be treated. Burning intensity was recorded through a visual analog scale before and after the treatment and at the 6-week follow-up. The percentage of the improvement in symptoms was also obtained. Results: Burning intensity at the end of the laser therapy was statistically lower than at the beginning (p < 0.01). Patients reported an 80.4% reduction in the intensity of symptoms after laser treatment. There was no statistical difference between the end of the treatment and the 6-week follow-up, except for the tongue site. Conclusion: Under the investigated parameters, infrared LLLT proved to be a valuable alternative for BMS treatment, providing a significant and lasting reduction in symptoms.

Molluscicidal and ovicidal activities of plant extracts of the Piperaceae on Biomphalaria glabrata (Say, 1818)

Schistosomiasis is a tropical disease caused by Schistosoma and occurs in 54 countries, mainly in South America, the Caribbean region, Africa and the eastern Mediterranean. Currently, 5 to 6 million Brazilian people are infected and 30,000 are under infection risk. Typical of poor regions, this disease is associated with the lack of basic sanitation and very frequently to the use of contaminated water in agriculture, housework and leisure. One of the most efficient methods of controlling the disease is application of molluscicides to eliminate or to reduce the population of the intermediate host snail Biomphalaria glabrata. Studies on molluscicidal activity of plant extracts have been stimulated by issues such as environmental preservation, high cost and recurrent resistance of snails to synthetic molluscicides. The aim of this study was to determine the molluscicide action of extracts from Piperaceae species on adult and embryonic stages of B. glabrata. Fifteen extracts from 13 Piperaceae species were obtained from stems, leaves and roots. Toxicity of extracts was evaluated against snails at two different concentrations (500 and 100 ppm) and those causing 100% mortality at 100 ppm concentration were selected to obtain the LC(90) (lethal concentration of 90% mortality). Piper aduncum, P. crassinervium, P. cuyabanum, P. diospyrifolium and P. hostmannianum gave 100% mortality of adult snails at concentrations ranging from 10 to 60 ppm. These extracts were also assayed on embryonic stages of B. glabrata and those from P. cuyabanum and P. hostmannianum showed 100% ovicidal action at 20 ppm.

Composition and screening of antifungal activity against Cladosporium sphaerospermum and Cladosporium cladosporioides of essential oils of leaves and fruits of Piper species

This study investigated the composition and antifungal activity against Cladosporium sphaerospermum and Cladosporium cladosporioides of essential oils of leaves of Piper cernuum, Piper diospyrifolium, Piper crassinervium, Piper solmsianum and Piper umbelata and fruits of P. cernuum and P. diospyrifolium. The essentials oils were analyzed by GC-MS and submitted of the antifungal activity tests. The essential oils of fruits from P. cernuum and leaves of P. crassinervium and P. solmsianum showed potential antifungal activity against C. sphaerospermum and C. cladosporioides. In addition, this is the first report of the composition of essential oils of fruits of P. cernuum and P. diospyrifolium.

Antimicrobial activity of Piper arboreum and Piper tuberculatum (Piperaceae) against opportunistic yeasts

In the scope of our ongoing research on bioactive agents from natural sources, 24 extracts and fractions obtained from Piper arboreum Aub. and Piper tuberculatum Jacq. ( Piperaceae) were screened for antifungal activity by using broth microdilution method. The current investigation reveals that P. arboreum extracts and fractions were more effective against Candida krusei and Candida parapsilosis than Cryptococcus neoformans. The growth of Candida albicans was weakly affected by all the tested extracts and fractions. The strongest effects were observed for hexane and ethyl acetate fractions from leaves of P. arboreum, with MIC values ( in mu g/ml) of 15.6 and 31.2 mu g/ml against C. krusei, respectively. Additionally, phytochemical investigation of the hexane fraction of P. arboreum leaves furnished 3 pyrrolidine amides; piperyline, 4,5-dihydropiperyline and tetrahydropiperyline, which could be responsible, at least in part for the observed antifungal activity. The most active compound, tetrahydropiperyline, displayed MIC values of 15.6 mu g/ml against C. krusei, C. parapsilosis and C. neoformans.

Intraspecific variability of dihydrochalcone, chromenes and benzoic acid derivatives in leaves of Piper aduncum L. (Piperaceae)

Chemical analysis carried out in leaves of 18 specimens of Piper aduncum L. (Piperaceae) occurring at Ripasa Reserve, Araraquara, SP, Brazil indicated two distinct populations when investigated over a period of 14 months (January 2000 to February 2001) and then submitted to cluster analysis. The two groups were characterized by accumulation of prenylated benzoic acids, chromenes and dihydrochalcone, respectively. A total of seven compounds were identified by HPLC analysis and compared with standards including two prenylated benzoic acid [aduncumene (1) and 3-(3'-7'-dimethyl-2'-6'-octadienyl)-4-methoxy-benzoic acid (5)], four chromenes [methyl 2,2-dimethyl-8-(3'-methyl-2'-butenyl)-2H-1-chromene-6-carboxylate (4), methyl 2,2-dimethyl-2H-1-chromene-6-carboxylate (2b), methyl 8-hydroxy-2,2-dimethyl-2H-1-chromene-6-carboxylate (3) and 2,2-dimethyl-2H-1-chromene-6-carboxylic acid (2a)] and one dihydrochalcone [2',6'-dihydroxy-4'-methoxy-dihydrochalcone (6)].

Study of Salmonella typhimurium mutagenicity assay of (E)-piplartine by the Ames test

Phytochemical studies carried out with Piperaceae species have shown great diversity of secondary metabolites among which are several displayed considerable biological activities. The species Piper tuberculatum has been intensively investigated and a series of amides have been described. For instance, (E)-piplartine showed significant cytotoxic activity against tumor cell lines, especially human leukemia cell lines; antifungal activity against Cladosporium species; trypanocidal activity and others. Considering the popular use of P. tuberculatum and the lack of pharmacological studies regarding this plant species, the mutagenic and antimutagenic effect of (E)-piplartine was evaluated by the Ames test, using the strains TA97a, TA98, TA100 and TA102 of Salmonella typhimurium. No mutagenic activity was observed for this compound.

Spectral properties of chaotic signals generated by the skew tent map

Chaotic signals have been considered potentially attractive in many signal processing applications ranging from wideband communication systems to cryptography and watermarking. Besides, some devices as nonlinear adaptive filters and phase-locked loops can present chaotic behavior. In this paper, we derive analytical expressions for the autocorrelation sequence, power spectral density and essential bandwidth of chaotic signals generated by the skew tent map. From these results, we suggest possible applications in communication systems. (C) 2009 Elsevier B.V. All rights reserved.

Spectral properties of chaotic signals with applications in communications

This paper investigates the characteristics of the Power Spectral Density (PSD) of chaotic signals generated by skew tent maps. The influence of the Lyapunov exponent on the autocorrelation sequence and on the PSD is evaluated via computational simulations. We conclude that the essential bandwidth of these signals is strongly related to this exponent and they can be low-pass or high-pass depending on the family`s parameter. This way, the PSD of a chaotic signal is a function of the generating map although this is not a one-to-one relationship. (C) 2009 Elsevier Ltd. All rights reserved.