bluuebunny/crossref_metadata_2025_split huggingface dataset:
Suspended in time? Peripheralised and “left behind” places in Germany
Authors: Royer Jeroen , Leibert Tim 
Published: August 2024

Abstract. The term “left behind” has regained attention with the increasing signs of political dissatisfaction in the Global North, e.g. the rise of right-wing populist parties and politicians. In Germany, terms such as abgehängte Regionen (suspended regions) or “structurally weak” regions are often employed as alternatives. However, there is a certain fuzziness in these terminologies, as they often encompass different spatial scales and temporal dependencies and refer to a variety of regions, e.g. deindustrialising cities as well as peripheral and remote rural areas. Our approach conceptualises “left-behindness” as an outcome of peripheralisation. This allows for a theory-based selection of social, economic, and infrastructural indicators to operationalise left-behindness in Germany at the NUTS3 (nomenclature of territorial units for statistics) level with combining a factor analysis and a k-means cluster analysis. The former resulted in four dimensions of left-behindness with distinct spatial patterns, leading to the classification of six regional types, characterised by varying scores for the four dimensions.
تطوير الوسائل بناء على أساس تطبيق بلوتاجون ستوري في تعليم اللغة العربية
Authors: Hasibuan Agita Yurinda , Rahmaini Rahmaini 
Published: August 2024

تحدث العديد من المشكلات في عملية التعليم، خاصة في وسائل التعليم المعتمدة على التكنولوجيا. يواجه العديد من المعلمين صعوبة في إنشاء الوسائط التعليمية، لذلك يستمرون في استخدام الأساليب التقليدية. بناءً على العوائق الموجودة في المدرسة المتوسطة الإسلامية الحكومية الأولى بسيمالجون، فإن أحد الحلول البديلة للتعامل معها هو تطبيق وسائط التعلم القائمة على التكنولوجيا، أي باستخدام وسائط التعلم القائمة على تطبيق الفيديو المتحرك، وهو بلوتاجون ستوري. يستخدم هذا البحث أسلوب (البحث والتطوير)، وهو أسلوب يمكنه إنتاج منتجات معينة ويتم اختبار فعاليته باستخدام نموذج ADDIE، وهو التحليل، التصميم، التطوير، التطبيق، التقييم. تظهر نتائج البحث أن النسبة التراكمية لاستجابات الطلاب لوسائل التعليم وصلت إلى ٪٩١ وكانت المعايير مثيرة للاهتمام للغاية، ولديها القدرة على توفير الابتكار في تعليم اللغة العربية.
Pengaruh Fleksibilitas Akuntansi Dan Pengungkapan Laporan Keuangan Terhadap Real Earning Management
Authors: Boniface Ata Donatus  , D Jefryan Christian Cabelen  , Tri Ratnawati  
Published: August 2024

This research purpose to examine influence of accounting flexibility, level of disclosure of financial statement and litigation risk to real earning management, this research also explore the role of audit quality to the relationship between accounting flexibility, level of disclosure of financial statement and litigation risk to real earning management. This research is done at the Indonesia Stock Exchange with population of 156 of manufacturing companies. The technical of sample taken by using the purposive sampling method, with 42 sample companies. The technique of data analysis use the SEM analysis with the aid of AMOS version 22. Result of this research show that accounting flexibility, level of disclosure of financial statement and litigation risk does not influence to real earning management, and also audit quality does not influence to the relationship between accounting flexibility, level of disclosure of financial statement and litigation risk to real earning management.
Partisipasi Masyarakat Lokal Sebagai Pelestarian Kesenian Bantengan di Desa Wisata Pandanrejo
Authors: Fahlevi Princes Arsarredima , Adnyana Made Bambang 
Published: August 2024

Makalah ini dibuat untuk mendeskripsikan kesenian yang ada di Desa Wisata Pandanrejo dan mengkaji sejauh mana partisipasi dan peran masyarakat Desa Pandanrejo sebagai pelestari budaya khususnya kesenian. Dalam makalah ini menggunakan pendekatan dan dijelaskan secara deskriptif. Untuk memahami serta menganalisis kesenian di Desa Pandanrejo dengan melakukan wawancara mendalam, observasi dan studi kepustakaan. Menganut teori partisipatif untuk menganalisis sejauh mana partisipasi dari masyarakat sebagai pelestari kesenian. Hasil penelitian menunjukkan bahwa masyarakat Desa Pandanrejo masih melakukan kesenian bantengan. Partisipasi kegiatan tradisi masyarakat Desa Samiran terdiri dari 2 jenis yaitu partisipasi aktif dan pasif. Dengan konsep pendekatan pariwisata berbasis masyarakat, kegiatan tradisi bisa menjadi daya tarik wisata budaya. Makalah ini mengusulkan peran masyarakat sebagai pelestari tradisi agar tetap dijaga dan dilestarikan.
Analisis Proses Rekruitmen Dan Seleksi Dalam Meningkatkan Kinerja Karyawan Pada PT.Mayora Indah,Tbk
Authors: Yeni Ariska  , Indah Fitri Fulkhanifah  , Carmidah Carmidah  
Published: August 2024

Penelitian ini bertujuan untuk menganalisis dan mendeskripsikan mengenai proses rekruitmen dan seleksi karyawan pada PT. Mayora. Penelitian ini merupakan penelitian kualitatif. Pengumpulan data menggunakan teknik wawancara pada salah satu karyawan (sebagai narasumber) yang bekerja di PT.Mayora. kemudian teknik analisis menggunakan teknik Miles dan Huberman yakni reduksi data, penyajian data dan verifikasi data. Hasil penelitian menunjukan bahwa proses rekruitmen pada PT.Mayora meliputi beberapa tahapan yaitu : mengalisis kebutuhan posisi yang dibutuhkan perusahaan, memasang berita lowongan pekerjaan diberbagai media, dan memproses lamaran pekerjaan yang telah diajukan si calon karyawan. Sedangkan untuk proses seleksinya pada PT.Mayora meliputi : psikotest, interview HRD, training MIDAS, interview user, tes kesehatan, pembuatan rekening dan probation/tes lapangan. Proses recruitmen dan seleksi tersebut bertujuan untuk meningkatkan kinerja karyawan pada PT.Mayora guna menjaga kualitas produk dan standard produk bermutu tinggi agar menjaga kepercayaan masyarakat akan produk makanan dan minuman pada PT.Mayora.
Pengaruh Price discount dan E-Word of Mouth Terhadap Purchase Decision Tiket Bioskop Melalui M-TIX
Authors: Bella Kalyana Putri  , Devianti Nurazizah  , Rifki Munawar  , Ramayani Yusuf  
Published: August 2024

The purpose of this study was to determine how Price discount and Electronic Word Of Mouth influence the Purchase Decision of Cinema Tickets through M-TIX. This study uses a descriptive type of analysis with quantitative methods. The entire Garut community became the population in this study, while 100 respondents became the sample. Saturated samples were used in this study. The data was collected using a questionnaire and analyzed using SPSS multiple regression analysis on Windows 25.0. The results showed that Price discount and E-Word Of Mouth can explain the Purchase Decision variable by 73.3%, while the remaining 26.7% is explained by other variables not included in the model.
Uma análise comparativa entre os contos Venha ver o pôr do sol, de Lygia Fagundes Teles e o Barril de Amontillado, de Edgar Allan Poe
Authors: Campos Gilson Felipe Teixeira , Costa Diana Barreto , Alves Claudilene de Sousa , Reis Luciana de Lima 
Published: August 2024

A partir do aporte teórico advindo da Literatura Comparada, este artigo analisa comparativamente os contos Venha ver o pôr do sol (1970), de Lygia Fagundes Teles, e O barril de Amontillado (1846), de Edgar Allan Poe. Esta pesquisa tem como objetivo comparar os dois contos, por meio das teorias usadas como métodos de análise, quais sejam: a apresentação de relações intertextuais e as dialógicas. Os procedimentos metodológicos adotados consistiram na revisão de literatura sobre o tema, apresentação de fragmentos que comprovem a presença do dialogismo entre as obras, e, ademais, a análise comparativa entre os textos. Conceitos como dialogismo e intertextualidade, derivados da teoria dialógica de Bakhtin (1929/1999) e estudados por Fiorin (2019), foram significativos para esta pesquisa. Por ser um estudo bibliográfico, os seguintes autores também foram consultados: Carvalhal (2006), Nitrini (2015), Jobim (2019), Koch, Bentes e Cavalcante (2012). Portanto, esta pesquisa apresenta as similaridades e diferenças entre as diegeses, a intertextualidade é explícita e inegável. O tema central dos contos é a vingança perfeitamente planejada e executada. Os resultados indicam uma relação dialógica permanente entre o texto da escritora brasileira e o conto do renomado e mundialmente conhecido escritor estadunidense, que foi pioneiro na escrita de contos de suspense e terror.
Herpes genital en gestantes de Latinoamérica, factores de riesgo, diagnóstico y prevención
Authors: Marcillo-Carvajal Carlos Pedro , López-Zambrano María José 
Published: August 2024

El herpes genital, ocasionado por el virus del herpes simple, ya sea del tipo 1 o 2, representa una infección de transmisión sexual prevalente, durante el embarazo, el herpes genital representa un riesgo significativo tanto para el desarrollo del feto como para el recién nacido. El objetivo principal fue Analizar el herpes genital en gestantes de Latinoamérica, factores de riesgo, diagnóstico y prevención. Se empleo una metodología con diseño de revisión sistemática documental, de tipo descriptivo. Entre los principales resultados se obtuvo que en Latinoamérica la prevalencia es del 11,2 y 30%, el país con mayor frecuencia de casos de herpes gestacional fue Brasil con más registros oscilando desde 59,99%: Los principales factores de riesgo fueron; la edad, infecciones previas, inmunosupresión, multiparidad, prematuridad, infección primaria de herpes, sexo sin protección: entre las diferentes técnicas diagnósticas para la detección de estos patógenos fueron la PCR cuantitativa, anticuerpos IgG IgM para VHS-1 y VHS-2,: la aplicación de vacunas profilácticas, profilaxis posexposicion, uso de preservativo, prácticas de sexo seguro, barreras protectivas, estas medidas ayudan a reducir el riesgo de transmisión: Se concluyo que en Latinoamérica varía significativamente entre los países, Brasil presenta la mayor frecuencia de casos: se identificaron varios factores de riesgo para el herpes genital en mujeres embarazadas, incluyendo la edad, infecciones previas: las diferentes técnicas diagnósticas para la detección de estos patógenos se encuentran la PCR cuantitativa; la aplicación de vacunas profilácticas, profilaxis post exposición, uso de preservativos, prácticas de sexo seguro y barreras protectoras, fueron medidas preventivas más aplicadas.
On a Zaremba’s Conjecture for Powers
Authors: Komatsu Takao 
Published: August 2024

A conjecture of Zaremba says that for every $m\ge 2$ there exists a reduced fraction $a/m$ such that its simple continued fraction has all its partial quotients bounded by $5$. This conjecture is proved with all partial quotients bounded by $3$ for $m$ being ${c\cdot 2^n}$-th power of $7$ where $n\ge 0$ and $c=1,3,5,7,9,11$. A more general case is considered.

2000 Mathematics Subject Classification. 11A55
Two Exponential Formulas for $\alpha$-Times Integrated Semigroups $\boldsymbol{(\alpha} \boldsymbol{\in} \boldsymbol{\mathbb{R}^ + )}$
Authors: Vajzović Fikret , Vugdalić Ramiz 
Published: August 2024

In this paper $X$ is a Banach space, $\left( {S(t)}\right) _{t\geq 0}$ is non-dege\-ne\-ra\-te $\alpha -$times integrated, exponentially bounded semigroup on $X$ $(\alpha \in \mathbb{R}^{+}),$ $M\geq 0$ and $\omega _{0}\in \mathbb{R}$ are constants such that $\left\| {S(t)}\right\| \leqslant Me^{\omega _{0}t}$ for all $t\geq 0,$ $\gamma $ is any positive constant greater than $\omega _{0},$ $\Gamma $ is the Gamma-function, $(C,\beta )-\lim $ is the Ces\`{a}ro-$\beta $ limit. Here we prove that\begin{equation*}\mathop {\lim }\limits_{n\rightarrow \infty }\frac{1}{{\Gamma(\alpha )}} \int\limits_{0}^{T}{(T-s)^{\alpha -1}\left({\frac{{n+1}}{s}}\right) ^{n+1}R^{n+1}\left({\frac{{n+1}}{s},A}\right) x\,ds=S(T)x,}\end{equation*}for every $x\in X,$ and the limit is uniform in $T>0$ on any bounded interval. Also we prove that\begin{equation*}S(t)x=\frac{1}{{2\pi i}}(C,\beta )-\mathop {\lim }\limits_{\omega\rightarrow \infty }\int\limits_{\gamma -i\omega }^{\gamma+i\omega }{ e^{\lambda t}\frac{{R(\lambda ,A)x}}{{\lambda^{\alpha }}}\,d\lambda },\end{equation*}for every $x\in X,\,\,\beta >0$ and $t\geq 0.$

2000 Mathematics Subject Classification. 47D06, 47D60, 47D62
A Generalization of Meir-Keeler Type Common Fixed Point Theorem For Four Noncontinuous Mappings
Authors: Popa Valeriu 
Published: August 2024

In this paper, using a combination of methods used in [1], [20] and [22] the results from [3, Theorem 1], [14, Theorem 1] and [15, Theorem 1] are improved removing the assumption of continuity, relaxing compatibility to the weak compatibility property and replacing the completeness of the space with a set of four alternative conditions for four functions satisfying an implicit relation.

2000 Mathematics Subject Classification. 54H25
Universality Results for Well-Founded Posets
Authors: Džamonja Mirna , Thompson Katherine 
Published: August 2024

In this paper it is shown that the univerality spectrum of well-founded posets is exactly the same as the spectrum of the class of well-orders. A universality result for a restricted class of well-founded posets under rank and order preserving embeddings is also proved. This is done using a club guessing method generalised by Kojman which demonstrates a surjective homomorphism with subsets of the reals of bounded size ordered by inclusion.

1991 Mathematics Subject Classification. 03E04, 06A05, 06A06
A Class of Functional Equations (Almost) Characterizing Polynomials on Integral Domains
Authors: Ebanks Bruce R. , De Place Friis Peter 
Published: August 2024

Let $R$ be an infinite integral domain not of characteristic 2. For a given $ n\geq 2$, suppose functions $f:R\rightarrow R$ and $h:R \rightarrow R$ satisfy\begin{equation*}[x_1,x_2,\ldots,x_n;f]=h(x_1+\cdots+x_n)\prod_{j>i}(x_j-x_i),\end{equation*}where the left side denotes the determinant of the $n\times n$ matrix with row $i$ given by $(1,x_i,x_i^2,\ldots,x_i^{n-2},f(x_i))$. It is proved that $ Df$ is a polynomial of degree at most $n$ over $R$, for some $D$ in $R$. For $n=2$ and $n=3$ the conclusion can be strengthened to take $D=1$, but surprisingly this is not possible for $n\geq 4$.

2000 Mathematics Subject Classification. Primary 39B52
The Kontorovich - Lebedev Transformation on Sobolev Type Spaces
Authors: Yakubovich Semyon B. 
Published: August 2024

The Kontorovich-Lebedev transformation $$(KLf)(x)=\int_0^\inftyK_{i\tau}(x)f(\tau)d\tau, \;\, x \in {\mathbf R}_+$$ is consideredas an operator, which maps the weighted space $L_p(\mathbf R_+;$$\omega(\tau)d\tau), \;\, 2 \le p \le \infty$ into the Sobolevtype space $S_p^{N, \alpha}({\mathbf R}_+)$ with the finite norm$$||u||_{S_p^{N,\alpha}({\mathbf R}_+)}= \biggl( \sum_{k= 0}^N\int_0^\infty |A_x^k u|^p x^{\alpha_k p -1} dx\biggr)^{1/p} <\infty,$$where $\alpha= (\alpha_0, \alpha_1, \dots, \alpha_N), \alpha_k \in{\mathbf R}, k=0, \dots, N$, and $ A_x$ is the differentialoperator of the form$$A_x u= x^2u(x) - x\frac{d}{dx}\biggl[x\frac{du}{dx }\biggr], $$and $A_x^k$ means $k$-th iterate of $A_x, \ A_x^0u= u$. Elementary properties for the space $S_p^{N, \alpha} ({\mathbf R}_+)$ are derived. Boundedness and inversion properties for the Kontorovich-Lebedev transform are studied. In the Hilbert case ($p=2$) the isomorphism between these spaces is established for the special type of weights and Plancherel's type theorem is proved.

2000 Mathematics Subject Classification. 44A15, 46E35, 26D10
Warped Product Lightlike Submanifolds
Authors: Şahin Bayram 
Published: August 2024

e study a new class of lightlike submanifolds $M$, called warped product lightlike submanifolds, of a semi-Riemann manifold. We show that the null geometry of $M$ reduces to the corresponding non-degenerate geometry of its semi-Riemann submanifold.

2000 Mathematics Subject Classification. 53C15, 53C40, 53C50
Regular Heptagon’s Midpoints Circle
Authors: Čerin Zvonko 
Published: August 2024

This paper explores the geometry of the regular heptagon $ABCDEFG$. We start from a classical result by Thébault and Demir that six midpoints of sides and diagonals lie on a cirlce m with diameter equal to the side of the square inscribed in the circumcircle of $ABCDEFG$. Then we discover eight more midpoints of segments on $m$ and show that they are vertices of two regular heptagons inscribed in the circle $m$. Extending further this idea we show that midpoints of many other segments also lie on the circle $m$ so that it deserves the name – the midpoints circle of $ABCDEFG$. In the proofs we use the complex numbers and perform our calculations with the help of computers in Maple V.

2000 Mathematics Subject Classification. Primary 51N20, 51M04, Secondary 14A25, 14Q05
Solutions of Neumann Boundary Value Problems for Higher Order Nonlinear Functional Difference Equations With $p$-Laplacian
Authors: Liu Yuji 
Published: August 2024

Sufficient conditions for the existence of at least one solution of Neumann boundary value problems for higher order nonlinear functional difference equations with $p$-Laplacian are established. We allow $f$ to be at most linear, superlinear or sublinear in the obtained results.

2000 Mathematics Subject Classification. 34B10, 34B15
The Diameter of a Zero-Divisor Graph for Finite Direct Product of Commutative Rings
Authors: Atani S. Ebrahimi , Kohan M. Shajari 
Published: August 2024

This paper establishes a set of theorems that describe the diameter of a zero-divisor graph for a finite direct product$R_{1}\times R_{2}\times\cdots\times R_{n}$ with respect to the diameters of the zero-divisor graphs of $R_{1},R_{2},\cdots,R_{n-1}$ and $R_{n}(n>2).$

2000 Mathematics Subject Classification. 05C75, 13A15
On Normal Subgroups of Unitary Groups of Some Unital ${AF}$-Algebras
Authors: Al-Rawashdeh Ahmed 
Published: August 2024

In the case of von Neumann factors of types $II_{1}$ and $III$, P. de la Harpe proved that, if $\mathcal{N}$ is a normal subgroup of the unitary group which contains a non-trivial self-adjoint unitary, then $\mathcal{N}$ contains all self-adjoint unitaries of the factor. In this paper, we prove that if $A$ is a unital $AF$-algebra, which is either a $UHF$-algebra or its dimension group $K_0(A)$ is a 2-divisible, then any normal subgroup of the unitary group contains all self-adjoint unitaries if it contains some certain non-trivial self-adjoint unitary. Afterwards, we prove that if two unitary group automorphisms agree on a normal subgroup $\mathcal{N}$ of the unitaries, which contains some certain non-trivial self-adjoint unitary, then they differ by some character on the unitary group of $A$.

2000 Mathematics Subject Classification. 46L05, 46L80, 16U60
Coincidence Points Under Weak Contractions on Symmetric Spaces
Authors: Latif Abdul , Abou-Hajar A. A. 
Published: August 2024

In this paper we prove some results on the existence of coincidence points for weak hybrid contractions on symmetric spaces. These results improve and generalize some known results. In particular, recent fixed point results due to Hicks [3] are generalized.

2000 Mathematics Subject Classification. 47H10, 54H25
On a Nonlinear Volterra-Fredholm Integral Equation
Authors: Pachpatte B. G. 
Published: August 2024

In this paper we study the existence, uniqueness and other properties of solutions of a certain nonlinear Volterra-Fredholm integral equation. The well known Banach fixed point theorem and the new integral inequality with explicit estimate are used to establish the results.

2000 Mathematics Subject Classification. 34K10, 35R10
Two Types of Multilinear Stieltjes Integrals in the Henstock-Kurzweil Sense
Authors: Halilović Armin 
Published: August 2024

In this paper we examine and compare two types of multilinear integrals considering their Stieltjes sums. The convergence of the Stieltjes sums is considered in the Riemann, Moore-Pollard and Henstock-Kurzweil sense.

2000 Mathematics Subject Classification. 28B05, 46G12
Existence Results for Nonoscillatory Solutions of Third Order Nonlinear Neutral Difference Equations
Authors: Thandapani E. , Karunakaran R. , Arockiasamy I. M. 
Published: August 2024

In this paper the authors consider the third order neutral difference equation\begin{equation*}\Delta ^{3}\left( x_{n}+p_{n}x_{n-k}\right) +q_{n}f\left(x_{n-\ell }\right) =h_{n}\end{equation*}where $\left\{ p_{n}\right\} ,\left\{ q_{n}\right\} ,\left\{h_{n}\right\} \ $are real sequences. They use Krasnoselskii's fixed point theorem to establish the existence of nonoscillatory solutions. The results are illustrated with examples.

2000 Mathematics Subject Classification. 39A10
On the Completion of Pro-$\mathcal{P}$ Groups
Authors: Ilić-Georgijević Emil 
Published: August 2024

We examine the class of finite paragraded groups which we will denote by $\mathcal{P}.$ After observing that the class $\mathcal{P}$ is closed with respect to subgroups and direct products (\cite{7}), we define the notion of a pro-$\mathcal{P}$ group and consider the completion of such a group.

2000 Mathematics Subject Classification. 08A05, 16W50, 20L05, 20E18, 20-99
Some New Grüss’ Type Inequalities for Functions of Selfadjoint Operators in Hilbert Spaces
Authors: Dragomir S. S. 
Published: August 2024

Some new inequalities of Grüss' type for functions of selfadjoint operators in Hilbert spaces, under suitable assumptions for the involved operators, are given. Several examples for particular functions of interest are provided as well.

2000 Mathematics Subject Classification. 47A63, 47A99
Curvature of the Focal Conic in the Isotropic Plane
Authors: Šimć M. , Volenec Vladimir , Brkić J. Beban 
Published: August 2024

It is shown in \cite{beba} that every focal conic $\mathcal{C}$ in the isotropic plane can be represented by the equation $y^2=\epsilon x^2+x$, $\epsilon \in \{-1,0,1\}$ and a parametrization. This paper gives the equation of the circle of curvature at the point $T$ of the focal conic $\mathcal{C}$. The radius of curvature $\rho$ at the point $T$ of the focal conic $\mathcal{C}$ is given as well as its relation to the span $\delta $ from the center of $\mathcal{C}$ to the tangent $\lijepot$ at the point $T$ and to the length of the half diameter of $\mathcal{C}$ on the diameter parallel to the $\textup{tangent}$.

2000 Mathematics Subject Classification. 51N25
Quasi-Diagonal Operators
Authors: Lohaj Muhib , Lohaj Shqipe 
Published: August 2024

Let $H$ be a separable complex Hilbert space and let $B(H)$ denote the algebra of all bounded linear operators on $H.$ If $T$ is a quasi-normal Fredholm operator we prove that $TT^*\in (QD)(P_n)$ if and only if $T^*T\in (QD)(P_n).$ We also show that if $T$ is quasi-normal and $T(T^*T)$ is quasi-diagonal with respect to any sequence $(P_n)$ in $PF(H),$ such that $P_n\rightarrow I$ strongly, then $T=N+K,$ where $N$ is a normal operator and $K$ is a compact operator.

2000 Mathematics Subject Classification. 47Bxx, 47B20
Translates of Sequences for Some Small Sets
Authors: Miller Harry I. , Miller-Van Wieren Leila 
Published: August 2024

D. Borwein and S. Z. Ditor have found a measurable subset $A$ of the real line having positive Lebesgue measure and a decreasing sequence $(d_n)$ of reals converging to $0$ such that, for each $x$, $x+d_n \notin A$ for infinitely many $n$. The set they constructed is nowhere dense. This result prompted us to further explore the question of subsets of $R$ and $R^{2}$ that are of "small size" and the existence of null sequences with the described property and hence attain some related results.

2000 Mathematics Subject Classification. 40D25, 40G99, 28A12
Analytic, Real Analytic and Harmonic Generalized Functions
Authors: Pilipović S. 
Published: August 2024

We recall definitions and assertions concerning the spaces noted in the title. Various classes of nonlinear problems can be studied within these spaces appropriate for the analysis of different kinds of singularities. Especially, we explain in this paper the notion of the generalized analytic wave front set.

2000 Mathematics Subject Classification. 46F10, 46S10, 35A27