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We consider the self-similar measure μ M , 𝒟 {\mu_{M,{\mathcal{D}}}} generated by an expanding real matrix M = ( ρ - 1 0 0 ρ - 1 ) ∈ M 2 ⁢ ( ℝ ) {M=\begin{pmatrix}\rho^{-1}&0\\ 0&\rho^{-1}\end{pmatrix}\in M_{2}({\mathbb{R}})} and a digit set 𝒟 = { ( 0 0 ) , ( a b ) , ( c d ) , ( a + c b + d ) } ⊆ ℤ 2 . {{\mathcal{D}}=\Biggl{\{}\begin{pmatrix}0\\ 0\end{pmatrix},\begin{pmatrix}a\\ b\end{pmatrix},\begin{pmatrix}c\\ d\end{pmatrix},\begin{pmatrix}a+c\\ b+d\end{pmatrix}\Biggr{\}}\subseteq{\mathbb{Z}}^{2}}. In this paper, we study the spectral and non-spectral problems of μ M , 𝒟 {\mu_{M,{\mathcal{D}}}} . In this case that ( a b ) {(\begin{smallmatrix}a\\ b\end{smallmatrix})} and ( c d ) {(\begin{smallmatrix}c\\ d\end{smallmatrix})} are two independent vectors, we prove that if ρ - 1 ∈ ℤ {\rho^{-1}\in{\mathbb{Z}}} , then μ M , 𝒟 {\mu_{M,{\mathcal{D}}}} is a spectral measure if and only if ρ - 1 ∈ 2 ⁢ ℤ {\rho^{-1}\in 2{\mathbb{Z}}} . For the case that ( a b ) {(\begin{smallmatrix}a\\ b\end{smallmatrix})} and ( c d ) {(\begin{smallmatrix}c\\ d\end{smallmatrix})} are two dependent vectors, we first give the sufficient and necessary condition for L 2 ⁢ ( μ M , 𝒟 ) {L^{2}(\mu_{M,{\mathcal{D}}})} to contain an infinite orthogonal set of exponential functions. Based on this result, we can give the exact cardinality of orthogonal exponential functions in L 2 ⁢ ( μ M , 𝒟 ) {L^{2}(\mu_{M,{\mathcal{D}}})} when L 2 ⁢ ( μ M , 𝒟 ) {L^{2}(\mu_{M,{\mathcal{D}}})} does not admit any infinite orthogonal set of exponential functions by classifying the values of ρ.

Background Whitefly Bemisia tabaci is a phloem-feeding insect and causes extensive agricultural damage around the world. Although the parasitic wasp Encarsia formosa is widely used to control B. tabaci on glasshouse tomatoes, low efficiency and discontinuity are frequently recorded. It has been well-documented that herbivore-induced plant volatiles (HIPVs) are important cues in the foraging behavior of the natural enemies of herbivores. However, the volatiles emitted from tomatoes infested by different developmental stages of B. tabaci (nymphs versus adults) have not been compared in terms of their effects on E. formosa attraction. Results Olfactometer assays with four tomato cultivars revealed that the E. formosa wasps showed a significant attraction to the volatiles from adult-infested plants (except for cv. Castlemart), but not to those from nymph-infested plants. In a close-range habitat, however, the wasps appeared to use visual or tactile cues derived from nymphs for host location. Volatile analyses and behavioral assays showed that wasp attraction was correlated with enhanced β-myrcene and β-caryophyllene emissions from adult-infested plants. Furthermore, the use of B. tabaci adult-induced plant cues under glasshouse conditions resulted in a higher parasitism rate by this parasitoid. Conclusion Our findings confirm that E. formosa uses the HIPVs resulting from feeding of B. tabaci adults to locate host habitat. Release of β-myrcene and β-caryophyllene from dispensers may enhance the efficacy of E. formosa as a biological control agent against B. tabaci in glasshouse production systems.

It is known that a set H of positive integers is a Poincare set (also called intersective set, see I. Ruzsa (1982)) if and only if $${\dim _\mathcal{H}}({X_H}) = 0$$ , where $${X_H}: = \left\{ {x = \sum\limits_{n = 1}^\infty {\frac{{{x_n}}}{{{2^n}}}:{x_n} \in \{ 0,1\} ,{x_n}{x_n} + h = 0\,for\,all\,n \geqslant 1,\,h \in H} } \right\}$$ and $${\dim _\mathcal{H}}$$ denotes the Hausdorff dimension (see C. Bishop, Y. Peres (2017), Theorem 2.5.5). In this paper we study the set XH by replacing 2 with b > 2. It is surprising that there are some new phenomena to be worthy of studying. We study them and give several examples to explain our results.

Let μ be a probability measure with compact support in R . The measure μ is called a spectral measure if there exists a countable set Λ ⊆ R , called a spectrum of μ, such that the family of exponential functions { e − 2 π i λ x : λ ∈ Λ } forms an orthonormal basis for L 2 ( μ ) . In this paper we study the structure of spectra and the real number t such that both Λ and tΛ are spectra for a class of self-similar spectral measures, which have symmetric spectra. Some examples are given to explain our theory.

Let $$\mu _{p,q}$$ be a self-similar spectral measure with consecutive digits generated by an iterated function system $$\{f_i(x)=\frac{x}{p}+\frac{i}{q}\}_{i=0}^{q-1}$$ , where $$2\le q\in {{\mathbb {Z}}}$$ and q|p. It is known that for each $$w=w_1w_2\cdots \in \{-1,1\}^\infty :=\{i_1i_2\cdots :~\text {all}~i_k\in \{-1,1\}\}$$ , the set $$\begin{aligned} \Lambda _w=\bigg \{\sum _{j=1}^{n}a_j w_j p^{j-1}:a_j\in \{0,1,\ldots ,q-1\},n\ge 1\bigg \} \end{aligned}$$ is a spectrum of $$\mu _{p,q}$$ . In this paper, we study the possible real number t such that the set $$t\Lambda _w$$ are also spectra of $$\mu _{p,q}$$ for all $$w\in \{-1,1\}^\infty $$ .

In this paper the authors study the Beurling dimension of Bessel sets and frame spectra of some self-similar measures on R d and obtain their exact upper bound of the dimensions, which is the same given by Dutkay et al. (2011) [8] . The upper bound is attained in usual cases and some examples are given to explain our theory.

We consider the equally-weighted Cantor measures μ p , q generated by the iterated function system (IFS) { f i ( x ) = x p + i q } i = 0 q − 1 , where 2 ≤ q ∈ Z and q p ∈ R . It is known that if q divides p, then μ p , q is a spectral measure with a spectrum Λ p , q = { 0 , 1 , … , q − 1 } + p { 0 , 1 , … , q − 1 } + p 2 { 0 , 1 , … , q − 1 } + ⋯ (finite sum) (Dai, He and Lai (2013) [6] ). In this paper the authors study some positive integers b such that b Λ p , q is also a spectrum of μ p , q .

In this paper, we continue the study in our previous work Beurling dimenison and self-similar measures [J. Funct. Anal. 274 (2018) 2245–2264]. We analyze the Beurling dimension of Bessel sequences and frame spectra of self-affine measures on [Formula: see text]. Unlike the case for the self-similar measures, it is very difficult to obtain a general expression for the dimension of self-affine sets. This implies that the Hausdorff dimension may be not a good candidate that controls the Beurling dimension in general. Instead, we find that the pseudo Hausdorff dimension proposed by He and Lau [Math. Nachr. 281 (2008) 1142–1158] can be a good candidate that can control the Beurling dimension. With the help of the pseudo Hausdorff dimension, we obtain the upper bounds of the Beurling dimension of Bessel sequences. Under suitable condition, we give the lower bound of the Beurling dimension of frame spectra of self-affine measures on [Formula: see text]. Some examples are given to illustrate our theory.

Let q = 4 r with integer r ≥ 1 . Let a = a 1 a 2 ⋯ , b = b 1 b 2 ⋯ ∈ { 0 , 1 , 2 , 3 } ∞ with a b , i.e., a n b n for all n ≥ 1 . We consider the following generalized Cantor measure μ q , a , b = δ 1 q { a 1 , b 1 } ⁎ δ 1 q 2 { a 2 , b 2 } ⁎ ⋯ , where δ E = 1 # E ∑ a ∈ E δ a denotes the uniformly discrete probability on E. In this paper we investigate the spectral eigenvalues (of the second type) of the measure μ q , a , b (the spectrality of μ q , a , b is settled by He et al. (2017) [17] ). More precisely, we characterize the possible real numbers t satisfying that there exists a countable set Λ ⊆ R such that Λ and tΛ are spectra of μ q , a , b simultaneously, i.e., the sets E ( Λ ) : = { e − 2 π i λ x : λ ∈ Λ } and E ( t Λ ) : = { e − 2 π i t λ x : λ ∈ Λ } are both orthonormal basis for L 2 ( μ q , a , b ) .

Trichogramma spp. are egg parasitoids largely used worldwide for biological control of lepidopteran pests. Host quality (related to host size and age, host species, etc.) can influence parasitism preference and fitness of the parasitoid offspring. However, few studies have documented the performance of Trichogramma parasitoids when they parasitize nonfertilized eggs of their lepidopteran hosts. In the present study, we investigated the performance of three indigenous Trichogramma species ( Trichogramma japonicum Ashmead, Trichogramma dendrolimi Matsumura, and Trichogramma chilonis Ishii) on fertilized and nonfertilized eggs of their native host, Chilo suppressalis (Walker). The results showed that the three Trichogramma species tested could recognize fertilized and nonfertilized eggs of C. suppressalis . The different fertilization status eggs of C. suppressalis were all accepted by T. japonicum , T. chilonis , and T. dendrolimi with a clear tendency that they preferred to parasitize fertilized eggs whether under no-choice or choice conditions. All Trichogramma species successfully completed development in parasitized eggs of C. suppressalis regardless if the host eggs were fertilized or not. There was similar adult emergence rate, development time, and female progeny between fertilized and nonfertilized eggs for all Trichogramma species with an exception of development for T. chilonis . Trichogramma chilonis had shorter developmental time in fertilized eggs than in nonfertilized ones. Whether in fertilized or nonfertilized eggs, T. dendrolimi had longer development time than other two Trichogramma species. However, T. dendrolimi had the largest percentage of female progeny on fertilized eggs, followed by T. japonicum , and T. chilonis had the least percentage of female progeny. The present study indicates that Trichogramma parasitoids (i) can distinguish fertilized vs. nonfertilized host eggs, and (ii) could use nonfertilized host eggs for successful offspring development (despite showing lower preference for such eggs) [corrected].

In the present paper, Pachycerina carinata sp. nov. is described as new to science and Pachycerina flaviventris Malloch, 1929 is newly recorded for China. A key to separate six species of the genus from China is presented.

An unreported disease of apricot was observed in orchards in Zhejiang province, China. Symptoms started as water soaked lesions on the fruit surface. Later, water-soaked areas developed and spread to the entire fruit, resulting in soft rot of the whole fruit. The causal organism isolated from symptomatic fruits was identified as Burkholderia cepacia based on its biochemical and physiological characteristics and confirmed by the cellular fatty acid composition and Biolog data as well as 16S rRNA gene sequence analysis. The bacterial isolates caused similar symptoms when inoculated onto fruits of apricot. In addition, European plum, Japanese plum, nectarine and kiwifruit were susceptible to the B. cepacia pathogen. However, the B. cepacia pathogen failed to cause any visible symptoms when it was inoculated onto 16 other fruits. This is the first report of a bacterial disease of apricot caused by B. cepacia in China.

Knowledge of water vapor and carbon dioxide (CO(2)) fluxes in agricultural lands is crucial to estimate carbon and water cycles as well as to investigate global warming potentials. In this study, the continuous wavelet transform technique along with cross-wavelet and wavelet coherence methods was applied to characterize half-hourly CO(2) flux (Fc) and water vapor (LE) flux data obtained with the eddy covariance technique in a summer maize field located in the North China Plain. our motivation was to highlight the multiple time scale properties and to exam the possible connections between the flux exchanges and the concurrent micro- meteorological variations. Results show that both Fc and LE could be characterized by the wavelet coefficients for the time scale ranged from 60-110 days. Peaks of CO(2) exchange were corresponded to the in-phase trough points of water vapor flux exchange rates on the 110 day, 64 day and 32 day time scales. Intra-seasonal oscillations in both water and CO(2) flux exchanges were associated with the patterns of photosynthetically active radiation, air temperature, vapor pressure deficient, and precipitation. Our study also showed that wavelet transfonns had prospect in making a physical explanation of the temporal structure of the flux exchanges between the crop biosphere and atmosphere in response to ambient variables. This study suggests that cross-wavelet analysis and wavelet coherence could be powerful methods for probing the dynamical relationship between the flux exchange and the dominant modes of climate variability. (C) 2008 Elsevier B.V. All rights reserved.

The correlation between constitutive and induced resistance to herbivores in plants has long been of interest to evolutionary biologists, and various approaches to determining levels of resistance have been used in this field of research. In this study, we examined the relationship between constitutive and induced resistance to the diamondback moth, Plutella xylostella (L.) (Lepidoptera: Plutellidae), in 11 closely related species of wild crucifers. We assessed the survival, development, and reproduction of the test insects and calculated their intrinsic rate of increase as an indicator of constitutive and induced resistance for the plants. We used larvae of P. xylostella and jasmonic acid as elicitors of the induced response. We failed to find a correlation between constitutive and induced resistance in these crucifer plants when the induction of resistance was initiated by either herbivory or jasmonic acid application. Analysis of the results suggests that the failure to detect a relationship between the two types of resistance could be caused by flaws in measuring constitutive resistance, which was apparently confounded with induced resistance. We discuss the difficulties and pitfalls in measuring constitutive resistance and ways to improve the methodology in investigating the relationships between constitutive and induced resistance in plants.

In phytophagous insects, experience can increase positive responses towards non-host plant extracts or induce oviposition on non-host plants, but the underlying chemical and behavioral mechanisms are poorly understood. By using the diamondback moth, Plutella xylostella, its host plant Chinese cabbage, and a non-host plant Chrysanthemum morifolium, as a model system, we observed the experience-altered olfactory responses of ovipositing females towards volatiles of the non-host plant, volatiles of pure chemicals (p-cymene and alpha-terpinene) found in the non-host plant, and volatiles of host plants treated with these chemicals. We assessed the experience-altered oviposition preference towards host plants treated with p-cymene. Naive females showed aversion to the odors of the non-host plant, the pure chemicals, and the pure chemical-treated host plants. In contrast, experienced females either became attracted by these non-host odors or were no longer repelled by these odors. Similarly, naive females laid a significantly lower proportion of eggs on pure chemical-treated host plants than on untreated host plants, but experienced females laid a similar or higher proportion of eggs on pure chemical-treated host plants compared to untreated host plants. Chemical analysis indicated that application of the non-host pure chemicals on Chinese cabbage induced emissions of volatiles by this host plant. We conclude that induced preference for previously repellent compounds is a major mechanism that leads to behavioral changes of this moth towards non-host plants or their extracts.

Least squares support vector machines (LS-SVMs), a nonlinear kernel based machine was introduced to investigate the prospects of application of this approach in modelling water vapor and carbon dioxide fluxes above a summer maize field using the dataset obtained in the North China Plain with eddy covariance technique. The performances of the LS-SVMs were compared to the corresponding models obtained with radial basis function (RBF) neural networks. The results indicated the trained LS-SVMs with a radial basis function kernel had satisfactory performance in modelling surface fluxes; its excellent approximation and generalization property shed new light on the study on complex processes in ecosystem.