Novos monômeros obtidos a partir do metacrilato de glicidila, bisfenol A e 4, 4 isopropilidenodicicloexanol : síntese, caracterização estrutural e propriedades de compósitos para utilização em resinas de restauração dental

Nowadays, composite resins are the direct restorative materials more important in dental clinical performance, due to their versatility and aesthetic excellence. Bis-GMA (2,2-bis[4(2-hydroxy-3-metacryloxypropoxy)phenil]propane) is the base monomer more frequently used in restorative composite resins. However, this monomer presents some disadvantages, such as high viscosity and two aromatic rings in its structure that can promote allergic reactions to the humans. In this work, the main purpose was to synthesize new monomers from glycidyl methacrylate to use in dental restorative materials. Structural characterization of the monomers was carried out through FTIR and NMR 1H, and eight composites were produced from the new monomers, by addition of silane-treated alumino silicate particles (inorganic filler) and a photocuring system (camphorquinone and ethyl 4-dimethylaminebenzoate). The composites were analyzed by environmental scanning electronic microscopy and the water sorption and solubility, compressive strength and elastic modulus were determined. A commercial composite resin [Z100 (3M)] was used to comparison effect. The new composites presented general characteristics similar to the commercial ones; however, they didn t present the properties expected. This behavior was attributed to the lower degree of monomer reaction and to the granulometry and size distribution of the mineral filler in the polymeric matrix

Novos monômeros obtidos a partir do metacrilato de glicidila, bisfenol A e 4, 4 isopropilidenodicicloexanol : síntese, caracterização estrutural e propriedades de compósitos para utilização em resinas de restauração dental

Nowadays, composite resins are the direct restorative materials more important in dental clinical performance, due to their versatility and aesthetic excellence. Bis-GMA (2,2-bis[4(2-hydroxy-3-metacryloxypropoxy)phenil]propane) is the base monomer more frequently used in restorative composite resins. However, this monomer presents some disadvantages, such as high viscosity and two aromatic rings in its structure that can promote allergic reactions to the humans. In this work, the main purpose was to synthesize new monomers from glycidyl methacrylate to use in dental restorative materials. Structural characterization of the monomers was carried out through FTIR and NMR 1H, and eight composites were produced from the new monomers, by addition of silane-treated alumino silicate particles (inorganic filler) and a photocuring system (camphorquinone and ethyl 4-dimethylaminebenzoate). The composites were analyzed by environmental scanning electronic microscopy and the water sorption and solubility, compressive strength and elastic modulus were determined. A commercial composite resin [Z100 (3M)] was used to comparison effect. The new composites presented general characteristics similar to the commercial ones; however, they didn t present the properties expected. This behavior was attributed to the lower degree of monomer reaction and to the granulometry and size distribution of the mineral filler in the polymeric matrix

Avaliação espectrofotométrica do manchamento de resinas odontológicas contendo nanopartículas

Composite resins have been subjected to structural modifications aiming at improved optical and mechanical properties. The present study consisted in an in vitro evaluation of the staining behavior of two nanohybrid resins (NH1 and NH2), a nanoparticulated resin (NP) and a microhybrid resin (MH). Samples of these materials were prepared and immersed in commonly ingested drinks, i.e., coffee, red wine and acai berry for periods of time varying from 1 to 60 days. Cylindrical samples of each resin were shaped using a metallic die and polymerized during 30 s both on the bottom and top of its disk. All samples were polished and immersed in the staining solutions. After 24 hours, three samples of each resin immersed in each solution were removed and placed in a spectrofotome ter for analysis. To that end, the samples were previously diluted in HCl at 50%. Tukey tests were carried out in the statistical analysis of the results. The results revealed that there was a clear difference in the staining behavior of each material. The nanoparticulated resin did not show better color stability compared to the microhybrid resin. Moreover, all resins stained with time. The degree of staining decreased in the sequence nanoparticulated, microhybrid, nanohybrid MH2 and MH1. Wine was the most aggressive drink followed by coffee and acai berry. SEM and image analysis revealed significant porosity on the surface of MH resin and relatively large pores on a NP sample. The NH2 resin was characterized by homogeneous dispersion of particles and limited porosity. Finally, the NH1 resin depicted the lowest porosity level. The results revealed that staining is likely related to the concentration of inorganic pa rticles and surface porosity

Avaliação espectrofotométrica do manchamento de resinas odontológicas contendo nanopartículas

Composite resins have been subjected to structural modifications aiming at improved optical and mechanical properties. The present study consisted in an in vitro evaluation of the staining behavior of two nanohybrid resins (NH1 and NH2), a nanoparticulated resin (NP) and a microhybrid resin (MH). Samples of these materials were prepared and immersed in commonly ingested drinks, i.e., coffee, red wine and acai berry for periods of time varying from 1 to 60 days. Cylindrical samples of each resin were shaped using a metallic die and polymerized during 30 s both on the bottom and top of its disk. All samples were polished and immersed in the staining solutions. After 24 hours, three samples of each resin immersed in each solution were removed and placed in a spectrofotome ter for analysis. To that end, the samples were previously diluted in HCl at 50%. Tukey tests were carried out in the statistical analysis of the results. The results revealed that there was a clear difference in the staining behavior of each material. The nanoparticulated resin did not show better color stability compared to the microhybrid resin. Moreover, all resins stained with time. The degree of staining decreased in the sequence nanoparticulated, microhybrid, nanohybrid MH2 and MH1. Wine was the most aggressive drink followed by coffee and acai berry. SEM and image analysis revealed significant porosity on the surface of MH resin and relatively large pores on a NP sample. The NH2 resin was characterized by homogeneous dispersion of particles and limited porosity. Finally, the NH1 resin depicted the lowest porosity level. The results revealed that staining is likely related to the concentration of inorganic pa rticles and surface porosity

Influência do pré-aquecimento na adaptação marginal de dois materiais seladores de fóssulas e fissuras, analisada através de tomografia de coerência ótica

Among the non-invasive techniques employed in the prevention of caries highlights the sealing pits and fissures which is a conservative maneuver, in order to obliterate them to protect them from attack acid bacteria. Influenced by the studies of pre-heating composite resin, which has experienced great improvement in some of their physical properties, this study aimed to evaluate in vitro the superficial and internal marginal adaptation of different materials and sealants in pre-heating or not. A total of 40 extracted human third molars (n=10) that had their occlusal surfaces prepared to receive sealant. We tested two types of sealing materials: resin sealant (Fluoroshield) and low-viscosity resin (Permaflo), where 50% of previously received heated material and the other half received sealant material at room temperature. All samples were subjected to thermal cycling and pH, simulating a cariogenic oral environment, and later were analyzed appliance OCT (optical coherence tomography). The images obtained alterations were recorded and analyzed statistically. Change was considered as the emergence of bubbles, gaps and cracks in the sealant. Comparisons of the same material, assessing the fact that it is not sealed or preheated material, as well as comparisons between different materials subjected to the same temperature were carried out. The nonparametric Tukey test was used (p < 0,05). The results showed that there was statistically significant difference between both the materials analyzed, as between the situations in which the sealant material was submitted (preheated or not). On the issue of marginal adaptation and internal surface, seen through Optical coherence tomography, may suggest that there is a difference between the use of one type or another of the sealing material analyzed, with superiority attributed to resin Permaflo compared to sealant Fluroshield, telling is the same for the different techniques used

Rugosidade superficial e adesão bacteriana em compósitos com nanopartículas após acabamento e polimento

Objective: To evaluate in vitro the surface roughness and bacterial adhesion of nanoparticle composites, after being subjected to different finishing and polishing systems. Materials and Methods: 66 specimens were prepared, and 30 with Filtek Z350 XT (3M ESPE, USA) and 30 with the resin IPS Empress Direct (Ivoclar Vivadent, USA), divided into 6 groups (n = 10 ). Six specimens were prepared for analysis in scanning electron microscopy (SEM) .Each kind of resin was subjected to finishing and polishing systems: Sof-Lex Pop-On discs (3M ESPE, USA) and AstropolTM system (Ivoclar Vivadent , USA), featuring the experimental group. The control group did not undergo any kind of finishing and polishing technique. The average roughness (Ra) in both groups was measured using a roughness in the setting of 0.25 mm (cut off) and surface images obtained with photomicrographs taken with a scanning electron microscope (SEM) magnified 500 times. Bacterial adherence was evaluated by determining the absorbance (OD) of the suspension of adhered cells by spectrophotometer at 570 nm. The results were submitted for analyzed with 2-way ANOVA at α=.05 and Tukey multiple comparison tests. Results: Statistically significant differences were found between the groups in terms of roughness and bacterial adhesion. Filtek Z350 XT for resin were no differences between the tested finishing and polishing systems, where the system of lowest surface roughness was the Sof-Lex Pop-On. To the resin IPS Empress Direct, the finishing and polishing system Astropol, had lower results of surface roughness. As for bacterial adhesion, the lowest optical density value for Filtek Z350 XT was for the group that used the finishing and polishing system Sof-Lex Pop-On and the resin IPS Empress Direct the group that used the Astropol system. In addition, there was a positive correlation between surface roughness and bacterial adhesion on polished surfaces (r = 0.612) Conclusions: surface roughness and bacterial adhesion are closely related. The finishing and polishing Sof-Lex Pop-On system is more suitable for nanoparticulate Filtek Z350 XT and the finishing and polishing system Astropol for resin nanohíbrida IPS Empress Direct.

Prevalência de oclusopatias e caracteríticas cefalométricas e dentais de escolares cearense da cidade de Fortaleza

The people of Ceará state are descended from miscegenation between the Portuguese colonizers and the native population, resulting in a different facial pattern from other populations. It is important that this pattern be thoroughly understood, along with its minimum and maximum values so that they can be assessed and respected, allowing professionals who deal with the craniofacial complex to work more efficiently and scientifically. Aim: To characterize the morphological pattern of individuals from Ceará state, whose father and grandfather are also native from Ceará, in the 10-12 year age group, not submitted to previous orthodontic treatment, in order to determine: 1) the prevalence of occlusal pattern; 2) the prevalence of dental anomalies (DA) and, 3) the skeletal and dental cephalometric characteristics of individuals that present with normal occlusion and harmonious facial pattern. Methodology: A list of 10-12 year-olds was obtained from 515 schools containing 162,713 students (Education Secretariat of Ceará State), from which 234 individuals were examined (107 boys and 157 girls). The assessment criteria adopted were: 1) Angle s Classification System to determine occlusal pattern. The occlusal characteristics were measured through overbite, overjet, crowding and interincisal diastema. 2) DA are anomalies of number, shape, size, eruption and structure and, 3) in the group that presented with normal occlusion, we used cephalometric analysis measures proposed by Downs, Steiner, Tweed, Holdaway, Jacobson and McNamara. Results: 1) 25.8% of the schoolchildren had normal occlusion, 47.5% class I malocclusion, 22.3% class II malocclusion and 4.2% class III malocclusion. No statistically significant difference was found between the age group studied and sex. Thirty percent of the individuals had normal overbite, while 36.7% and 19.7% had increased and reduced overbite, respectively. Normal overjet was found in 33.7% of the individuals, increased overjet in 50% and reduced in 16.3%. Dental crowding was observed in 62.5% of the individuals and the presence of interincisal diastema in 14.8%. 2) The prevalence of DA was 56.1%, 6.8% in the number, 10.8% in shape, 4.1% in size, 34.5% in eruption, 26.4% in structure and 17.4% had more than one DA. No association was found between DA and sex, but DA was significantly associated to malocclusion (p<0.05); 3) there was no association between sex or facial type between the measures of nasal-labial angle, position and effective maxillary length, effective mandibular length and the sagittal relationship between the molars, overjet and overbite, position of upper incisors, lower incisors and between the incisors themselves. There was a difference between sex, on the VERT index and in lower anterior facial height, upper incisor inclination and line-H, between facial types for the occlusal plane angles, mandibular plane, facial axis, lower incisor inclination, mandibular position, upper incisor position, lower anterior facial height, ANB and line-H. It was concluded that: 1) the most prevalent occlusal type was class I malocclusion, with no distinction for sex or age group, and the assessment of occlusal characteristics showed that excessive overbite and overjet were the most predominant findings, along with a high occurrence of tooth crowding; 2) a high prevalence of DA was found, particularly eruption anomalies, not influenced by sex but significantly associated to malocclusion and 3) individuals from Ceará are predominantly brachyfacial, exhibiting a number of similarities inherent to their facial pattern, such as a convex profile, retracted jaw, reduced lower third and protruded lower incisors. This study was multidisciplinary, involving researchers from the areas of epidemiology, radiology and dentistry, thereby meeting the multidisciplinarity requirements of the Postgraduate Program in Health Sciences

Imunoexpressão das claudinas -1 e -7 em ameloblastomas e germes dentais humanos

We investigated the immunohistochemistry expression of claudins -1 and -7 in ameloblastoma and in human dental germs on the pattern of distribution (focal, regional or diffuse), the cells that expressed (if central or peripheral) and the location of that expression in the cell components recital membrane, cytoplasm and nucleus. Among the 29 cases of ameloblastoma, 24 were type solid and 6 unicystic. In 7 mandibular specimens of human fetuses found dental germs from the stage of bud to the crown. We note that the pattern of expression in the dental germs was variable for claudinas studied according to the cell type and stage of differentiation and was invariate only in the cells of stellate reticulum. In epithelium internal of enamel organ, claudin-1 has been decreasing with the progression of differentiation as to claudina-7 that was found in the cells of the peripheral papilla. For ameloblastoma the expression was more significant than that observed in dental germs. Fisher s exact test no found association between the expression of claudinas cells in central and peripheral and the type of ameloblastoma (solid or unicystic). Thus, in general the claudin-1 was positive in the central cell of 93,1% of the cases and in peripheral cells of 51,7%. The claudin-7 was expressed in the cells of all cases central and peripheral cells from 89,7%. For both claudins the distribution was predominantly diffuse cells both in central and peripheral cells. Given our findings it is suggested that the expression of claudins may be indicative of the involvement of these molecules in morphogenetics events culminating with the dental development and that possibly influence the development of neoplastic ameloblastoma

Preparação de resinas de poliuretana à base de óleo de mamona e dietanolamina

The aim of this work was the preparation of polyols from reactions between castor oil and dietanolamine to increase the hydroxyl content and the network degree in the products to application in electronic devices. The polyols and the mixtures obtained were characterized by nuclear magnetic ressonance. Castor oil (CO) is a natural triglyceride - based polyol possessing hydroxyl groups, which allow several reactions that produce many different products. Among them are the polyurethanes (PU), which have been considered an ideal product for the covering of electricelectronic circuits, due to their excellent electrical, shock-absorbing, solvents resistance and hydrolytic stability properties. About 90% of the fatty acids present in the castor oil are ricinoleic acid (12-hydroxyoleic acid), while the remaining 10% correspond to non-hydroxylated fatty acids, mainly linoleic and oleic acids. The chemical analysis of castor oil indicates a hydroxyl number of 2.7. In this work, a polyol was obtained by the reaction of the CO with diethanolamine (DEA), in order to elevate the hydroxyl value from 160 to 230 or to 280 mgKOH/g, and characterized by nuclear magnetic resonance (NMR) 1H and 13C (Mercury 200). The polyadition of the resulting polyol with isophorone diisocianate (IPDI) was carried out at 60°C, and the reaction kinetics was followed by rheological measurements in a Haake RS150 rheometer. The electrical properties were determined in a HP LCR Meter 4262A, at 1.0 Hz and 10.0 KHz. The chemical analysis showed that the polyols obtained presented hydroxyl number from 230 to 280 mgKOH/g. The polyadition reaction with IPDI produced polyurethane resins with the following properties: hardness in the range from 45 shore A to 65 shore D (ASTM D2240); a dielectric constant of 3.0, at 25°C (ASTM D150). Those results indicate that the obtained resins present compatible properties to the similar products of fossil origin, which are used nowadays for covering electric-electronic circuits. Therefore, the PUs from castor oil can be considered as alternative materials of renewable source, free from the highly harmful petroleum - derived solvents

Estudo do desempenho de resinas poliméricas para remoção de H2S do gás natural

The natural gas (NG) is a clean energy source and found in the underground of porous rocks, associated or not to oil. Its basic composition includes methane, ethane, propane and other components, like carbon dioxide, nitrogen, hydrogen sulphide and water. H2S is one of the natural pollutants of the natural gas. It is considered critical concerning corrosion. Its presence depends on origin, as well as of the process used in the gas treatment. It can cause problems in the tubing materials and final applications of the NG. The Agência Nacional do Petróleo sets out that the maximum concentration of H2S in the natural gas, originally national or imported, commercialized in Brazil must contain 10 -15 mg/cm3. In the Processing Units of Natural Gas, there are used different methods in the removal of H2S, for instance, adsorption towers filled with activated coal, zeolites and sulfatreat (solid, dry, granular and based on iron oxide). In this work, ion exchange resins were used as adsorbing materials. The resins were characterized by thermo gravimetric analysis, infrared spectroscopy and sweeping electronic microscopy. The adsorption tests were performed in a system linked to a gas-powered chromatograph. The present H2S in the exit of this system was monitored by a photometrical detector of pulsing flame. The electronic microscopy analyzes showed that the topography and morphology of the resins favor the adsorption process. Some characteristics were found such as, macro behavior, particles of variable sizes, spherical geometries, without the visualization of any pores in the surface. The infrared specters presented the main frequencies of vibration associated to the functional group of the amines and polymeric matrixes. When the resins are compared with sulfatreat, under the same experimental conditions, they showed a similar performance in retention times and adsorption capacities, making them competitive ones for the desulphurization process of the natural gas

Estudo do desempenho de resinas poliméricas para remoção de H2S do gás natural

The natural gas (NG) is a clean energy source and found in the underground of porous rocks, associated or not to oil. Its basic composition includes methane, ethane, propane and other components, like carbon dioxide, nitrogen, hydrogen sulphide and water. H2S is one of the natural pollutants of the natural gas. It is considered critical concerning corrosion. Its presence depends on origin, as well as of the process used in the gas treatment. It can cause problems in the tubing materials and final applications of the NG. The Agência Nacional do Petróleo sets out that the maximum concentration of H2S in the natural gas, originally national or imported, commercialized in Brazil must contain 10 -15 mg/cm3. In the Processing Units of Natural Gas, there are used different methods in the removal of H2S, for instance, adsorption towers filled with activated coal, zeolites and sulfatreat (solid, dry, granular and based on iron oxide). In this work, ion exchange resins were used as adsorbing materials. The resins were characterized by thermo gravimetric analysis, infrared spectroscopy and sweeping electronic microscopy. The adsorption tests were performed in a system linked to a gas-powered chromatograph. The present H2S in the exit of this system was monitored by a photometrical detector of pulsing flame. The electronic microscopy analyzes showed that the topography and morphology of the resins favor the adsorption process. Some characteristics were found such as, macro behavior, particles of variable sizes, spherical geometries, without the visualization of any pores in the surface. The infrared specters presented the main frequencies of vibration associated to the functional group of the amines and polymeric matrixes. When the resins are compared with sulfatreat, under the same experimental conditions, they showed a similar performance in retention times and adsorption capacities, making them competitive ones for the desulphurization process of the natural gas

Análise microbiológica da cavidade interna de implantes dentais osseointegrados utilizando o checkerboard DNA-DNA hybridization

Introduction: Infiltration of organic fluids and microorganisms at the abutment/implant interface may result in bacterial infection of peri-implant tissues. Internal colonization of periodontal pathogens may be caused by bacteria trapped during installation or penetration of abutment/implant leakage. The aim of this study was to detect periodontal pathogens in the internal area of dental implants before loading. Materials and Methods: Seventy-eight implants in 32 partially edentulous subjects were selected for this evaluation. A bacterial biofilm sample of the internal surface of each implant was taken and analyzed for the presence of 40 microorganisms by checkerboard DNA-DNA hybridization, prior to installation of healing or any other prosthetic abutment. Discussion: Bacteria were detected in 20 patients (62.5%), distributed in 41 implants (52.6%). Forty-seven percent of implants showed no bacterial detection. Spontaneous early implant exposure to oral cavity during the healing period was not significant (P >0.05) to increase bacterial prevalence, but implants placed at mandible had higher bacterial prevalence than maxillary ones. Conclusion: The internal surface of dental implants can serve as a reservoir of periodontal pathogens for future implant/abutment interface.

Técnicas estendidas para saxofone em obras compostas por meio de colaboração compositor-intérprete

This dissertation deals with the use of extended techniques for the saxophone in the piece Minus (for solo saxophone in Bb), composed through a composer-performer collaboration between Agamenon de Morais and the saxophonist Kleber Dessoles. The text is organized in the following manner: the first part brings the historical background of the concert music written for the saxophone since the beginning of the 20th-century, exploring the use of extended tehcniques and the main characters and historical facts of this period, with data obtained through a literature review; the second part deals with the issue of the composer-performer collaboration, since cases documented in the 18th and 19th centuries until nowadays, exploring in which different ways collaborations may happen and the motivations behind them; the third and final part is about the specific work, followed by a detailed description of the collaboration between the composer and the interpreter, as well as detailed explanations about the extended techniques present in the work (multiphonics and flatterzunge), through bibliographic and documental research, as well as descriptions of the meetings between composer and interpreter. At the end of the collaborative process, one may say that the final result was created from a sum of the composer's knowledge with the interpreter's, almost as if the composition had double authorship. The document describing this process may help composers and interpreters in composing for the saxophone, as well as guide future collaborative experiences.

Autoeficácia, características sociodemográficas e capacitação profissional: um estudo com servidores de uma Universidade Federal

Self-efficacy, the construct developed by Albert Bandura in 1977 and widely studied around the world, means the individual's belief in his own capacity to successfully perform a certain activity. This study aims to determine the degree of association between sociodemographic characteristics and professional training to the levels of Self-Efficacy at Work (SEW) of the Administrative Assistants in a federal university. This is a descriptive research submitted to and approved by the Ethics Committee of UFRN. The method of data analysis, in quantitative nature, was accomplished with the aid of the statistical programs R and Minitab. The instrument used in research was a sociodemographic data questionnaire, variables of professional training and the General Perception of Self-efficacy Scale (GPSES), applied to the sample by 289 Assistants in Administration. Statistical techniques for data analysis were descriptive statistics, cluster analysis, reliability test (Cronbach's alpha), and test of significance (Pearson). Results show a sociodemographic profile of Assistants in Administration of UFRN with well-distributed characteristics, with 48.4% men and 51.6% female; 59.9% of them were aged over 40 years, married (49.3%), color or race white (58%) and Catholics (67.8%); families are composed of up to four people (75.8%) with children (59.4%) of all age groups; the occupation of the mothers of these professionals is mostly housewives (51.6%) with high school education up to parents (72%) and mothers (75.8%). Assistants in Administration have high levels of professional training, most of them composed two groups of servers: the former, recently hired public servants (30.7%) and another with long service (59%), the majority enter young in career and it stays until retirement, 72.4% of these professionals have training above the minimum requirement for the job. The analysis of SEW levels shows medium to high levels for 72% of assistants in administration; low SEWclassified people have shown a high average of 2.7, considered close to the overall mean presented in other studies, which is 2.9. The cluster analysis has allowed us to say that the characteristics of the three groups (Low, Medium and High SEW) are similar and can be found in the three levels of SEW representatives with all the characteristics investigated. The results indicate no association between the sociodemographic variables and professional training to the levels of self-efficacy at work of Assistants in Administration of UFRN, except for the variable color or race. However, due to the small number of people who declared themselves in color or black race (4% of the sample), this result can be interpreted as mere coincidence or the black people addressed in this study have provided a sense of efficacy higher than white and brown ones. The study has corroborated other studies and highlighted the subjectivity of the self-efficacy construct. They are needed more researches, especially with public servants for the continuity and expansion of studies on the subject, making it possible to compare and confirm the results

análise experimental do efeito da diversificação em carteiras de ações: a relação entre risco e quantidade de ativos sob a ótica da estratégia ingênua

The objective is to analyze the relationship between risk and number of stocks of a portfolio for an individual investor when stocks are chosen by "naive strategy". For this, we carried out an experiment in which individuals select actions to reproduce this relationship. 126 participants were informed that the risk of first choice would be an asset average of all standard deviations of the portfolios consist of a single asset, and the same procedure should be used for portfolios composed of two, three and so on, up to 30 actions . They selected the assets they want in their portfolios without the support of a financial analysis. For comparison we also tested a hypothetical simulation of 126 investors who selected shares the same universe, through a random number generator. Thus, each real participant is compensated for random hypothetical investor facing the same opportunity. Patterns were observed in the portfolios of individual participants, characterizing the curves for the components of the samples. Because these groupings are somewhat arbitrary, it was used a more objective measure of behavior: a simple linear regression for each participant, in order to predict the variance of the portfolio depending on the number of assets. In addition, we conducted a pooled regression on all observations by analyzing cross-section. The result of pattern occurs on average but not for most individuals, many of which effectively "de-diversify" when adding seemingly random bonds. Furthermore, the results are slightly worse using a random number generator. This finding challenges the belief that only a small number of titles is necessary for diversification and shows that there is only applicable to a large sample. The implications are important since many individual investors holding few stocks in their portfolios